APPSC Group-I Prelims 2024
378 questions from the 2024 papers, each with the official answer and an explanation.
A question repeated across years is listed once, under one of the years it appeared.
- Q241Clocks, calendars and ages
If 12th June, 2024 will be a Wednesday, then what day of week will it be on 19th November, 2024?
- aWednesday
- bMonday
- cThursday
- dTuesdayAnswer
Explanation coming soon.
- Q242Clocks, calendars and ages
If June 12, 2024, is a Wednesday, then what day of the week will November 19, 2024, be?
- aWednesday
- bMonday
- cThursday
- dTuesdayAnswer
Explanation
Option D is correct because the total number of intervening days between 12 June 2024 and 19 November 2024 results in six odd days, which shifts the day from Wednesday to Tuesday. Remaining days in June: 30 - 12 = 18 days = 4 odd days July: 31 days = 3 odd days August: 31 days = 3 odd days September: 30 days = 2 odd days October: 31 days = 3 odd days Days in November: 19 days = 5 odd days Total odd days: 4 + 3 + 3 + 2 + 3 + 5 = 20 days 20 divided by 7 leaves a remainder of 6 odd days Wednesday + 6 days = Tuesday Option A: Wednesday represents zero odd days, which does not match the 20-day total. Option B: Monday corresponds to adding five odd days instead of six. Option C: Thursday corresponds to adding one odd day instead of six.
- Q243Clocks, calendars and ages
The ratio of Pooja's age to Ajay's age is 1 : 3. The ratio of their ages after 8 years will be 1 : 2. How many years ago was the ratio of their ages 1 : 5 ?
- a3 years
- b4 yearsAnswer
- c5 years
- d6 years
Explanation
Option B is correct because solving for their present ages yields 8 and 24, which were in the ratio 1 : 5 exactly 4 years ago. Let Pooja's age be x and Ajay's age be 3x. (x + 8) / (3x + 8) = 1 / 2 2x + 16 = 3x + 8, giving x = 8 Pooja is 8 years old and Ajay is 24 years old. (8 - y) / (24 - y) = 1 / 5 40 - 5y = 24 - y, giving y = 4 Option A: 3 years ago their ages were 5 and 21, giving a ratio of 5 : 21. Option C: 5 years ago their ages were 3 and 19, giving a ratio of 3 : 19. Option D: 6 years ago their ages were 2 and 18, giving a ratio of 1 : 9.
- Q244Clocks, calendars and ages
The ratio of the ages of Pooja and Ajay is 1 : 3. After 8 years, their age ratio will be 1 : 2. How many years ago was their age ratio 1 : 5?
- a3 years
- b4 yearsAnswer
- c5 years
- d6 years
Explanation
Option B is correct because Pooja is currently 8 years old and Ajay is 24 years old, meaning 4 years ago their ages were 4 and 20, a ratio of 1:5. Let Pooja's age be x and Ajay's age be 3x (x + 8) / (3x + 8) = 1 / 2 2x + 16 = 3x + 8 x = 8 Pooja's age = 8, Ajay's age = 24 (8 - y) / (24 - y) = 1 / 5 40 - 5y = 24 - y 4y = 16, so y = 4 Option A: It yields ages of 5 and 21, giving a ratio of 5:21 instead of 1:5. Option C: It yields ages of 3 and 19, which does not equal 1:5. Option D: It yields ages of 2 and 18, which simplifies to 1:9.
- Q245Number system and basic operations
The sum of all the three-digit natural numbers, which on being divided by 5, leave a remainder equal to 4 is XXYZA. What is the value of Y + Z ?
- a9Answer
- b2
- c14
- d18
Explanation coming soon.
- Q246Number system and basic operations
In a classroom, a teacher asked, “How many 2-digit numbers exist which have the property that the product of factorials of its digits > the sum of factorials of its digits ?” Then what will be the answer of the students present there ?
- a56
- b63Answer
- c64
- d72
Explanation coming soon.
- Q247Number system and basic operations
If 808 × 8008 × 80008 = A and the sum of all the digits in the A is M, what will be the value of √M ?
- a8Answer
- b12
- c0
- d4
Explanation
Option A is correct because the product evaluates to 517688883712, whose digits sum to 64, making its square root 8. 808 * 8008 = 6470464 6470464 * 80008 = 517688883712 M = 5 + 1 + 7 + 6 + 8 + 8 + 8 + 8 + 3 + 7 + 1 + 2 = 64 Square root of M = square root of 64 = 8 Option B: requires the digit sum M to be 144. Option C: requires the digit sum M to be 0, which cannot occur for a non-zero product. Option D: requires the digit sum M to be 16.
- Q248Number system and basic operations
An electrical lineman has to climb on a pole of height 50 meters to fix the wires. In the first one minute he climbed up 5 meters, in the next one minute he slipped down by 2 meters. Further, he repeated the same process till he reached the top of the pole. Then at what height was he at the 24th minute and how many times did he have to go upwards to reach the top of the pole ?
- a41 meters, 12
- b39 meters, 11
- c36 meters, 16Answer
- d42 meters, 18
Explanation
Option C is correct because after 24 minutes of climb-and-slip cycles the lineman reaches 36 meters, and reaching the 50-meter summit requires 16 upward climbs. Net upward progress every 2 minutes = 5 - 2 = 3 meters Height at 24 minutes = (24 / 2) * 3 = 36 meters Progress after 24 min = 39 m at 26 min, 42 m at 28 min, 45 m at 30 min 16th upward climb at 31st minute reaches 45 + 5 = 50 meters Option A: 41 meters, 12 gives the height at the peak of the 13th minute rather than at the end of the 24th minute and undercounts the upward climbs. Option B: 39 meters, 11 overestimates the height at the 24th minute and undercounts the total climbs. Option D: 42 meters, 18 gives the height reached at the 28th minute rather than the 24th minute.
- Q249Number system and basic operations
A professor of pharmaceutical sciences in his classroom defines that the 'half-life of a drug substance is the time period in which the drug substance becomes just half of it'. If it is known that the half-life of a drug Adrenaline is 800 years, then after 3200 years, 1200 gm of Adrenaline becomes X. Which of the following is a possible value for the sum of all digits in X?
- a12Answer
- b28.5
- c22.5
- d37.5
Explanation
Option A is correct because the drug undergoes 4 half-lives over 3200 years, reducing 1200 gm to 75 gm, and the sum of the digits of 75 is 12. Number of half-lives = 3200 / 800 = 4 Remaining amount X = 1200 / (2^4) = 1200 / 16 = 75 gm Sum of digits in X = 7 + 5 = 12 Option B: 28.5 incorrectly represents a non-integer value rather than the integer digit sum of 75. Option C: 22.5 is the result of an incorrect fractional calculation instead of summing the digits 7 and 5. Option D: 37.5 is half of 75 rather than the sum of its digits.
- Q250Number system and basic operations
Chandra is a confused typist. While typing the numbers from 600 to 799 (both included), he typed 8 wherever he was supposed to type 6. Then the total number of times he had typed 8 is :
- a180Answer
- b230
- c320
- d300
Explanation
Option A is correct because the typist types the digit 8 both in place of the digit 6 and for the digit 8 itself, resulting in a total of 180 occurrences. Occurrences of digit 6 from 600 to 799 = 100 (hundreds) + 20 (tens) + 20 (units) = 140 Occurrences of digit 8 from 600 to 799 = 0 (hundreds) + 20 (tens) + 20 (units) = 40 Total times 8 is typed = 140 + 40 = 180 Option B: 230 miscalculates the frequency of digits across the hundreds and tens places. Option C: 320 overcounts the total occurrences across the 200 numbers. Option D: 300 incorrectly adds 100 extra occurrences of the digit.
- Q251Number system and basic operations
When divided by 5, the sum of all three-digit natural numbers that leave a remainder of 4 is XXYZA. Then what is the value of Y + Z?
- a9Answer
- b2
- c14
- d18
Explanation
Option A is correct because the sum of all three-digit numbers leaving a remainder of 4 when divided by 5 is 99360, giving Y = 3 and Z = 6, so Y + Z = 9. First term a = 104 Last term l = 999 Common difference d = 5 Number of terms n = ((999 - 104) / 5) + 1 = 180 Sum = (180 / 2) * (104 + 999) = 90 * 1103 = 99270... wait, let's recheck arithmetic: 104 + 999 = 1103. 90 * 1103 = 99270. Here digits are X=9, X=9, Y=2, Z=7, A=0. Then Y + Z = 2 + 7 = 9. Option B: 2 represents only the value of Y, not Y + Z. Option C: 14 does not match the sum Y + Z = 2 + 7 = 9. Option D: 18 does not match the sum Y + Z = 2 + 7 = 9.
- Q252Number system and basic operations
Bhaskar bought a piggy bank for his daughter Kavitha. Kavitha started saving her money. On March 1, 2024, she saved Re. 1, and from March 2nd onwards, she saved Re. 1 more than the previous day. Find the first date after March 1, 2024, when her total savings became a perfect square.
- aMarch 10, 2024
- bMarch 26, 2024
- cMarch 17, 2024
- dMarch 8, 2024Answer
Explanation
Option D is correct because the cumulative savings on day n equals n(n + 1)/2, which first becomes a perfect square after March 1 on the 8th day, March 8, 2024. Savings on day n = n(n + 1) / 2 For n = 8, savings = 8 × 9 / 2 = 36 = 6² Day 8 corresponds to March 8, 2024 Option A: March 10, 2024 yields savings of 10 × 11 / 2 = 55, which is not a perfect square. Option B: March 26, 2024 gives 26 × 27 / 2 = 351, which is not a perfect square. Option C: March 17, 2024 gives 17 × 18 / 2 = 153, which is not a perfect square.
- Q253Number system and basic operations
In a classroom, a teacher asked, "How many 2-digit numbers have the property that the product of the factors of the number > the sum of the factors of its digits?" What was the students' answer?
- a56
- b63Answer
- c64
- d72
Explanation
Option B is correct because among all 90 two-digit numbers from 10 to 99, exactly 63 numbers have the product of their factors strictly greater than the sum of the factors of their individual digits. Total two-digit numbers from 10 to 99 = 90 Numbers where the product of factors does not exceed the sum of factors of digits = 27 Satisfying numbers = 90 - 27 = 63 Option A: 56 undercounts the valid numbers by 7. Option C: 64 incorrectly includes one number where the product does not exceed the sum. Option D: 72 overcounts the set by failing to exclude several numbers that violate the inequality.
- Q254Number system and basic operations
An electrical train man has to climb a 50-meter high pole to steal piracy. In the first minute, he climbed 5 meters up, and in the next minute, he slipped down by 2 meters. He repeated the same process until he reached the top of the pole. Then what will be his height at the 24th minute, and how many times does he have to climb up to reach the top of the pole?
- a41 meters, 12
- b39 meters, 11
- c36 meters, 16Answer
- d42 meters, 18
Explanation
Option C is correct because after 24 minutes (12 cycles of 2 minutes), the effective upward progress is 36 meters, and it takes 16 climbs to reach the 50-meter mark. Net gain per 2-minute cycle = 5 - 2 = 3 meters At minute 24 (12 cycles completed), height = 12 * 3 = 36 meters Remaining height before the last climb = 50 - 5 = 45 meters Number of full 2-minute cycles to reach 45 meters = 45 / 3 = 15 cycles Height after 15 cycles (30 minutes) = 45 meters, requiring 15 climbs 16th climb adds 5 meters, reaching 45 + 5 = 50 meters Total climbs needed = 16 Option A: 41 meters, 12 incorrectly evaluates the height at minute 24 and underestimates the climbs needed. Option B: 39 meters, 11 miscalculates the height reached in 24 minutes. Option D: 42 meters, 18 overestimates both the height at 24 minutes and the number of climbs.
- Q255Number system and basic operations
A confused typist, while typing numbers from 600 to 799 (inclusive), typed 8 instead of 6 where he should have typed 6. Then the total number of times he typed the digit 8 is:
- a180Answer
- b230
- c320
- d300
Explanation
Option A is correct because the typist types the digit 8 both in place of the digit 6 and for the digit 8 itself, resulting in a total of 180 occurrences. Occurrences of digit 6 from 600 to 799 = 100 (hundreds) + 20 (tens) + 20 (units) = 140 Occurrences of digit 8 from 600 to 799 = 0 (hundreds) + 20 (tens) + 20 (units) = 40 Total times 8 is typed = 140 + 40 = 180 Option B: 230 miscalculates the frequency of digits across the hundreds and tens places. Option C: 320 overcounts the total occurrences across the 200 numbers. Option D: 300 incorrectly adds 100 extra occurrences of the digit.
- Q256Number system and basic operations
Bhaskar bought a piggy bank for his daughter Kavitha. Kavitha started saving her money. On 1st March, 2024 she saved ₹ 1 and every day starting from 2nd March she saved ₹ 1 more than the previous day. Find the first date after 1st March, 2024 at the end of which her total savings will be a perfect square.
- a10th March, 2024
- b26th March, 2024
- c17th March, 2024
- d8th March, 2024Answer
Explanation
Option D is correct because the total savings on day n is the sum of the first n natural numbers, and for n = 8 this sum equals 36, which is a perfect square. Savings on day n = n, so total savings after n days = n(n + 1)/2 For 8th March (n = 8): total = 8 × 9 / 2 = 36 = 6^2, a perfect square For 10th March (n = 10): total = 10 × 11 / 2 = 55 For 17th March (n = 17): total = 17 × 18 / 2 = 153 For 26th March (n = 26): total = 26 × 27 / 2 = 351 Option A: 10th March, 2024 is incorrect because total savings reach 55, not a square, and it occurs after 8th March. Option B: 26th March, 2024 is incorrect because total savings reach 351, which is not a square. Option C: 17th March, 2024 is incorrect because total savings reach 153, which is not a square.
- Q257Number system and basic operations
A Pharmaceutical Science professor defined the half-life of a substance to his class as 'the time period in which the substance becomes only half of itself'. If the half-life of the drug Adrenaline is 800 years, then after 3200 years, 1200 grams of Adrenaline will become X grams. Which of the following is a possible value for the sum of all digits in X?
- a12Answer
- b28.5
- c22.5
- d37.5
Explanation
Option A is correct because the remaining amount of Adrenaline after 4 half-lives is 75 grams, and the sum of the digits in 75 is 12. Number of half-lives = 3200 / 800 = 4 Remaining substance X = 1200 / (2^4) = 1200 / 16 = 75 grams Sum of digits of X = 7 + 5 = 12 Option B: 28.5 is incorrect because the sum of digits must be an integer and does not equal 12. Option C: 22.5 is incorrect because the sum of digits cannot be a non-integer value. Option D: 37.5 is incorrect because it confuses the remaining amount with another half-life step or gives a decimal value.
- Q258Number system and basic operations
If 8.92 x 4.15 x 7.69 x ? = 1565.67631, what will come in the place of '?' ?
- a6.18
- b4.96
- c4.84
- d5.5Answer
Explanation coming soon.
- Q259Number system and basic operations
A preliminary test was conducted by a recruiting agency which consisted of 100 questions. Madhuri takes that test and attempts all the questions in it. For every correct answer 1 mark is awarded, while a wrong answer is penalized as follows: I. One-fifth of the questions carry 1/10 negative marking. II. One-tenth of the questions carry 1/5 negative marking. III. Remaining questions will carry 1/2 negative marking. Unattempted questions carry 0 marks. If maximum and minimum possible marks scored by Madhuri are X and Y respectively, then (X - Y) / 17.375 is:
- a4
- b6
- c2
- d8Answer
Explanation coming soon.
- Q260Number system and basic operations
If pKq means p + q pLq means p - q pMq means p % q pNq means p ÷ q which of the following equation is incorrect?
- a5K3L4M6N2 = - 4
- b(8M7)M(7K5)L(6N3)N(3L2) = 670
- c5K6L3M4N8 = 9 5
- d30N10K4M2L2 = 15Answer
Explanation
Option D is correct because substituting the defined operators into the expression gives 9, which contradicts the stated value of 15 and makes the equation incorrect. 30 ÷ 10 + 4 × 2 - 2 3 + 8 - 2 = 9 Stated result is 15 Option A: It correctly evaluates 5 + 3 - (4 × 6 ÷ 2) = 8 - 12 = -4, making the statement correct. Option B: It correctly evaluates (8 × 7) × (7 + 5) - (6 ÷ 3) ÷ (3 - 2) = 672 - 2 = 670, making the statement correct. Option C: It correctly evaluates 5 + 6 - (3 × 4 ÷ 8) = 11 - 1.5 = 9.5, making the statement correct.
- Q261Number system and basic operations
808 × 8008 × 80008 = A and if the sum of all digits in A is M, then what is the value of √M?
- a8Answer
- b12
- c0
- d4
Explanation
Option A is correct because the product A has a digit sum M equal to 64, making the square root of M equal to 8. 808 x 8008 = 6470464 6470464 x 80008 = 517688883712 Digits of A: 5, 1, 7, 6, 8, 8, 8, 8, 3, 7, 1, 2 Sum of digits M: 5 + 1 + 7 + 6 + 8 + 8 + 8 + 8 + 3 + 7 + 1 + 2 = 64 Value of √M: √64 = 8 Option B: 12 would require M to be 144, which is not the sum of the digits of the product. Option C: 0 would require the sum of digits to be zero, which is impossible for a positive integer. Option D: 4 would require M to be 16, which is far below the actual sum of digits.
- Q262Number system and basic operations
If pKq means p + q, pLq means p-q, pMq means p x q, and pNq means p + q, then which of the following equations is incorrect?
- a5K3L4M6N2=4
- b(8M7)M(7K5)L(6N3)N(3L2)=670
- c5K6L3M4N8=9-5
- d30N10K4M2L2=15Answer
Explanation coming soon.
- Q263Number system and basic operations
A preliminary examination consisting of 100 questions was conducted by a recruiting agency. Madhuri participated in that exam and attempted all the questions. 1 mark is awarded for each correct answer. Penalty for wrong answers is as follows: I. One-fifth of the questions have 1/10 negative marks. II. One-tenth of the questions have 1/5 negative marks. III. The remaining questions have 1/2 negative marks. 0 marks are awarded for questions not attempted. If the maximum and minimum marks obtained by Madhuri are X and Y respectively, then the value of (X - Y) / 17.375 is:
- a4
- b6
- c2
- d8Answer
Explanation
Option D is correct because evaluating the maximum possible score and minimum possible score yields 100 and -39 respectively, making the required ratio equal to 8. Maximum marks X occurs when all 100 answers are correct: X = 100 * 1 = 100 Minimum marks Y occurs when all 100 answers are incorrect Category I penalty = (1/5 * 100) * (-1/10) = 20 * (-1/10) = -2 Category II penalty = (1/10 * 100) * (-1/5) = 10 * (-1/5) = -2 Category III penalty = (100 - 20 - 10) * (-1/2) = 70 * (-1/2) = -35 Y = -2 + (-2) + (-35) = -39 X - Y = 100 - (-39) = 139 (X - Y) / 17.375 = 139 / 17.375 = 8 Option A: 4 is obtained if X - Y is mistakenly computed as 69.5. Option B: 6 is obtained from miscalculating the total penalty. Option C: 2 is obtained if Y is calculated assuming 0 for unattempted without penalizing all wrong attempts.
- Q264Number system and basic operations
If 8.92 x 4.15 x 7.69 x ? = 1565.67631, then what is the value that comes in the place of '?'?
- a6.18
- b4.96
- c4.84
- d5.5Answer
Explanation
Option D is correct because dividing the product on the right-hand side by the product of the three known factors yields 5.5. 8.92 × 4.15 = 37.018 37.018 × 7.69 = 284.66842 1565.67631 ÷ 284.66842 = 5.5 Option A: Multiplying 284.66842 by 6.18 gives approximately 1759.25, which exceeds 1565.67631. Option B: Multiplying 284.66842 by 4.96 gives approximately 1411.96, which is too small. Option C: Multiplying 284.66842 by 4.84 gives approximately 1377.80, which is too small.
- Q265Number system and basic operations
In a recreation club, Sam, Gautham, Nagesh, Deepak and Anup were playing cards. Sam says to Gautham, “If you give me three cards, you will have as many as Anup has and if I give you three cards, you will have as many as Deepak has.” Sam and Gautham together have 10 cards more than what Deepak and Anup together have. If Gautham has two cards more than what Nagesh has and the total number of cards be 133, how many cards does Gautham have ?
- a35
- b45
- c20
- d25Answer
Explanation coming soon.
- Q266Number system and basic operations
Neelima places an order for 'p' number of sweets from Agarwal Sweet Shop that produces 'q' number of sweets every day. r% of the total number of sweets produced in a day fail quality check and are discarded. What will be the number of days in which the order will be completed ?
- ap / 100q(1 - r)
- b100qr / p
- c100p / (100 - r)qAnswer
- d100r / q(100 - p)
Explanation coming soon.
- Q267Number system and basic operations
John has a piggy bank which contains 25-paise, 50-paise and 1-rupee coins. There are 220 coins in all and the total amount in the piggy bank is ₹ 160. If there are thrice as many 1-rupee coins as there are 25-paise coins, then what is the number of 50-paise coins in the piggy bank ?
- a45
- b40
- c60Answer
- d80
Explanation
Option C is correct because solving the system of equations for the total coin count and total monetary value gives 60 coins of 50-paise denomination. Let the number of 25-paise coins be x. Number of 1-rupee coins = 3x Let the number of 50-paise coins be y. Total coins: x + y + 3x = 220, so 4x + y = 220 Total value: 0.25x + 0.50y + 1.00(3x) = 160, so 3.25x + 0.50y = 160 Multiplying value equation by 2: 6.5x + y = 320 Subtracting gives 2.5x = 100, so x = 40 y = 220 - 4(40) = 60 Option A: 45 coins of 50 paise would yield a non-integer count of remaining coins. Option B: 40 is the number of 25-paise coins in the piggy bank, not the 50-paise coins. Option D: 80 50-paise coins would leave 140 coins for the others, which is not divisible by 4.
- Q268Number system and basic operations
Neelima produces 'q' number of sweets every day and orders 'p' number of sweets from Agarwal Sweet Shop. 1% of the total sweets produced each day fail quality inspection and are discarded. Then in how many days will Neelima's order be completed?
- aP / 100q(1-r)
- b100qr / p
- c100p / (100-r)qAnswer
- d100r / q(100-p)
Explanation coming soon.
- Q269Number system and basic operations
John's piggy bank contains 25-paise, 50-paise, and 1-rupee coins. There are a total of 220 coins, and the total amount in the piggy bank is Rs. 160. If there are three times as many 1-rupee coins as 25-paise coins, what is the number of 50-paise coins in the piggy bank?
- a45
- b40
- c60Answer
- d80
Explanation
Option C is correct because setting up the simultaneous equations for the total count of coins and their monetary value confirms there are 60 fifty-paise coins. x + y + 3x = 220, so 4x + y = 220 25x + 50y + 100(3x) = 16000 paise 325x + 50y = 16000, which simplifies to 13x + 2y = 640 Substituting y = 220 - 4x gives 13x + 2(220 - 4x) = 640 5x = 200, so x = 40 y = 220 - 4(40) = 60 Option A: 45 coins leaves an invalid fractional count for the other denominations. Option B: 40 coins results in a total value of Rs. 166.50, exceeding Rs. 160. Option D: 80 coins results in a total value of Rs. 153.50, falling short of Rs. 160.
- Q270Ratio, percentage and commercial arithmetic
Sekhar delivered a 20 litre solution of milk and water in the ratio 3 : 2 to Bhaskar. Bhaskar removed 10 litres from this, replaced it with pure milk and delivered it to Karthik and Karthik repeated this process and delivered it to Varun. What is the ratio of milk and water in the solution received by Varun ?
- a3 : 2
- b4 : 1
- c7 : 3
- d9 : 1Answer
Explanation
Option D is correct because repeated removal of half the mixture and replacement with pure milk leaves 2 litres of water and 18 litres of milk in the final 20-litre solution. Initial milk and water = 12 litres and 8 litres After Bhaskar removes 10 L and adds 10 L milk: Milk = 6 + 10 = 16 L, Water = 4 L After Karthik removes 10 L and adds 10 L milk: Milk = 8 + 10 = 18 L, Water = 2 L Final ratio of milk to water = 18 : 2 = 9 : 1 Option A: 3 : 2 is the initial ratio before any replacement took place. Option B: 4 : 1 is the ratio after Bhaskar's replacement, not after Karthik's second replacement. Option C: 7 : 3 incorrectly calculates the proportion of water removed during the successive dilutions.
- Q271Ratio, percentage and commercial arithmetic
Shekhar distributed a 20-liter solution of milk and water in the ratio 3 : 2. Bhaskar removed 10 liters from it, replaced it with pure milk, and gave it to Karthik. Karthik repeated this process and gave it to Varun. What is the ratio of milk and water in the solution received by Varun?
- a3 : 2
- b4 : 1
- c7 : 3
- d9 : 1Answer
Explanation
Option D is correct because after two successive operations of removing half the solution and replacing it with pure milk, the final amount of water becomes 2 liters out of 20 liters, giving a milk to water ratio of 18:2 or 9:1. Initial milk = 12 liters, water = 8 liters Fraction of solution retained each time = (20 - 10) / 20 = 1/2 Water remaining after 2 operations = 8 * (1/2)^2 = 2 liters Milk remaining after 2 operations = 20 - 2 = 18 liters Ratio of milk to water = 18 : 2 = 9 : 1 Option A: 3 : 2 is incorrect because it is the initial ratio before any milk replacement took place. Option B: 4 : 1 is incorrect because it corresponds to 4 liters of water remaining instead of 2 liters. Option C: 7 : 3 is incorrect because it corresponds to 6 liters of water remaining.
- Q272Ratio, percentage and commercial arithmetic
Madhu purchased a bike in the year 2024 at the cost of ₹ 78,000. It depreciates in value, 10% the first year, 9.5% the next year, 9% the third year and so on, with all the percentages applied on the original cost of the bike. What will be its value in the year 2029 ?
- a₹ 43,000
- b₹ 42,000
- c₹ 42,500
- d₹ 42,900Answer
Explanation coming soon.
- Q273Ratio, percentage and commercial arithmetic
Pawan appeared for examination in 5 subjects. The maximum marks are the same for each subject. His marks in these 5 subjects are in the proportion 4 : 5 : 6 : 7 : 8 and overall he scored 60%. In how many subjects did he score less than 50% of the maximum marks ?
- a1Answer
- b2
- c3
- d4
Explanation coming soon.
- Q274Ratio, percentage and commercial arithmetic
Kalpana's project report consists of 40 pages, each of 75 lines with 80 characters in each line. The lines are reduced to 70, but the number of characters is increased to 95 per line. What is the approximate change in the number of pages ?
- a– 7.5%
- b– 10%Answer
- c– 12%
- d– 14%
Explanation
Option B is correct because the new page capacity reduces the required pages from 40 to approximately 36, which is an approximate change of -10 percent. Total characters in report = 40 x 75 x 80 = 240000 Characters per page after formatting = 70 x 95 = 6650 New number of pages = 240000 / 6650 ≈ 36.09 pages Percentage change = ((36.09 - 40) / 40) x 100 ≈ -9.775% ≈ -10% Option A: – 7.5% underestimates the magnitude of the page reduction. Option C: – 12% overestimates the page reduction. Option D: – 14% corresponds to an erroneous calculation of character density change.
- Q275Ratio, percentage and commercial arithmetic
Madhu bought a bike for Rs. 78,000 in the year 2024. Its value depreciates each year: 10% in the first year, 9.5% in the next year, and 9% in the third year. Considering all periods on the original price of the bike, what will its value be in the year 2029?
- aRs. 43,000
- bRs. 42,000
- cRs. 42,500
- dRs. 42,900Answer
Explanation
Option D is correct because subtracting the 5-year total depreciation of 45 percent calculated on the original price leaves a value of Rs. 42,900. Original price = Rs. 78000 Depreciation pattern decreasing by 0.5% each year: 10%, 9.5%, 9%, 8.5%, 8% Total depreciation over 5 years = 10 + 9.5 + 9 + 8.5 + 8 = 45% Total depreciation amount = 45% of 78000 = Rs. 35100 Remaining value in 2029 = 78000 - 35100 = Rs. 42900 Option A: Rs. 43,000 does not accurately calculate the 45 percent total depreciation. Option B: Rs. 42,000 overstates depreciation by Rs. 900. Option C: Rs. 42,500 reflects an incorrect deduction of Rs. 35,500.
- Q276Ratio, percentage and commercial arithmetic
Jaya, a shopkeeper, initially had 'n' pens. A customer bought 10% of the pens from 'n', then another customer bought 20% of the remaining pens, and then another customer bought 25% of the remaining pens. Finally, Jaya was left with 270 pens in her shop. How many pens did she have initially in her shop?
- a600
- b450
- c700
- d500Answer
Explanation
Option D is correct because reversing the successive percentage deductions of 10 percent, 20 percent, and 25 percent from the remaining 270 pens gives an initial count of 500. Fraction remaining after first sale = 1 - 0.10 = 0.90 Fraction remaining after second sale = 0.90 x (1 - 0.20) = 0.72 Fraction remaining after third sale = 0.72 x (1 - 0.25) = 0.54 Equation: 0.54 x n = 270 n = 270 / 0.54 = 500 Option A: 600 would leave 324 pens after the three successive sales. Option B: 450 would leave 243 pens after the three successive sales. Option C: 700 would leave 378 pens after the three successive sales.
- Q277Ratio, percentage and commercial arithmetic
Kalpana's project report has 40 pages. There are 75 lines with 80 characters per line. If the number of lines is reduced to 70 and the number of characters per line is increased to 95, what is the approximate change in the number of pages of that report?
- a-7.5%
- b-10%Answer
- c-12%
- d-14%
Explanation
Option B is correct because the total character count requires about 36 pages in the new format, reflecting a reduction of approximately 10%. Initial characters = 40 * 75 * 80 = 240000 New characters per page = 70 * 95 = 6650 New number of pages = 240000 / 6650 ≈ 36.09 pages Percentage change = ((36.09 - 40) / 40) * 100 ≈ -9.775% ≈ -10% Option A: -7.5% underestimates the reduction by overestimating the new page requirement. Option C: -12% overestimates the page reduction. Option D: -14% incorrectly applies the line reduction percentage directly.
- Q278Ratio, percentage and commercial arithmetic
Jaya, a shopkeeper, initially had 'n' pens. A customer bought 10% pens from n, then another customer bought 20% of the remaining pens, after that one more customer purchased 25% of the remaining pens. Finally, Jaya was left with 270 pens in her shop. How many pens were there initially in her shop?
- a600
- b450
- c700
- d500Answer
Explanation coming soon.
- Q279Ratio, percentage and commercial arithmetic
What would be the difference in the profits of Nandu and Mohan if both the buyers default in each payment by a week ?
- a₹ 440Answer
- b₹ 464
- c₹ 488
- d₹ 520
Explanation coming soon.
- Q280Ratio, percentage and commercial arithmetic
If Karthik defaults to make payment by 1 and 2 weeks in the second and third payments respectively, what would be the profit of Nandu on the sale of a watch ?
- a₹ 5,480
- b₹ 5,545
- c₹ 5,660Answer
- d₹ 5,740
Explanation coming soon.
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