Question 1

Twenty persons complete one-third (1/3) of a job in 12 days. How many additional persons are needed to complete the remaining work in the next 12 days (assume equal efficiency)?

Accepted Answer

Introduction / Context: This is a standard manpower scaling question: if a certain team completes a fraction in a certain time, we determine how many workers are necessary to complete the remainder in a specified time, assuming uniform efficiencies. Given Data / Assumptions: 20 persons complete 1/3 of work in 12 days. Remaining work = 2/3. Desired remaining duration = 12 days. Worker efficiencies are equal and constant. Concept / Approach: Compute one person’s daily work rate from the first phase. Use it to find the total number of persons required for the second phase. Subtract existing 20 to get “additional” persons required. Step-by-Step Solution: Let r = one person’s daily work. From first phase: 20 * r * 12 = 1/3 ⇒ r = 1 / 720. For remaining 2/3 in 12 days with N persons: N * r * 12 = 2/3. Substitute r: N * (1/720) * 12 = 2/3 ⇒ N / 60 = 2/3 ⇒ N = 40. Additional persons needed = 40 − 20 = 20. Verification / Alternative check: With 40 persons: 40 * (1/720) * 12 = 2/3 as required. Why Other Options Are Wrong: 12, 15, 18, 40 do not reflect the “additional” headcount computed; 40 is the total requirement, not the increment. Common Pitfalls: Confusing total required with extra required; not deriving the per-person rate first. Final Answer: 20

Question 2

A and B together can complete a job in 15 days. B alone can complete it in 20 days. In how many days can A alone complete the job?

Accepted Answer

Introduction / Context: When you know the combined time and one individual’s time, you can find the other’s rate by subtracting rates, then invert to find the time for the other individual alone. Given Data / Assumptions: A + B = 15 days. B alone = 20 days. Rates are constant and additive. Concept / Approach: Convert times to rates: r(A+B) = 1/15; r(B) = 1/20. Then r(A) = r(A+B) − r(B). Finally, A’s time = 1 / r(A). Step-by-Step Solution: r(A+B) = 1/15 per day. r(B) = 1/20 per day. r(A) = 1/15 − 1/20 = (4 − 3)/60 = 1/60. A’s time = 1 / (1/60) = 60 days. Verification / Alternative check: Check: 1/60 + 1/20 = 1/60 + 3/60 = 4/60 = 1/15. Correct. Why Other Options Are Wrong: 30, 35, 40, 45 days do not satisfy the rate equations with the given combined time of 15 days. Common Pitfalls: Averaging days directly; forgetting that rates (not times) add. Final Answer: 60 days

Question 3

A and B can complete a piece of work in 6 days together, and A alone can complete it in 9 days. How many days will B alone take to complete the same work?

Accepted Answer

Introduction / Context: Another rate subtraction problem: from the combined rate and one individual’s rate, the other’s rate can be found and inverted to get the corresponding time. Given Data / Assumptions: A + B = 6 days ⇒ r(A+B) = 1/6 per day. A alone = 9 days ⇒ r(A) = 1/9 per day. Concept / Approach: r(B) = r(A+B) − r(A). Then B’s time = 1 / r(B). Step-by-Step Solution: r(B) = 1/6 − 1/9 = (3 − 2)/18 = 1/18. B’s time = 1 / (1/18) = 18 days. Verification / Alternative check: 1/9 + 1/18 = 2/18 + 1/18 = 3/18 = 1/6, confirming the combined time of 6 days. Why Other Options Are Wrong: 12, 15, 7.5, 20 days do not yield a combined time of exactly 6 days with A’s 9 days rate. Common Pitfalls: Averaging the times; forgetting to add rates; arithmetic slips with fractions. Final Answer: 18 days

Question 4

A and B can do a job in 18 days, B and C in 24 days, and A and C in 36 days. If all three work together, in how many days will the job be completed?

Accepted Answer

Introduction / Context: Pairwise completion times can be used to extract the sum of individual rates and hence the time for all three working together. This is a standard system-of-rates technique. Given Data / Assumptions: (A+B) = 18 days ⇒ r(A)+r(B) = 1/18. (B+C) = 24 days ⇒ r(B)+r(C) = 1/24. (C+A) = 36 days ⇒ r(C)+r(A) = 1/36. Concept / Approach: Add the three equations: 2[r(A)+r(B)+r(C)] = 1/18 + 1/24 + 1/36. Then divide by 2 to get r(A)+r(B)+r(C), the combined rate for all three. Step-by-Step Solution: Sum RHS with denominator 72: 1/18=4/72, 1/24=3/72, 1/36=2/72. Total = 9/72 = 1/8. Hence 2[r(A)+r(B)+r(C)] = 1/8 ⇒ r(A)+r(B)+r(C) = 1/16. Therefore, time together = 1 / (1/16) = 16 days. Verification / Alternative check: The pairwise rates are consistent; the derived combined rate 1/16 satisfies all constraints and is a common textbook result pattern. Why Other Options Are Wrong: 12, 13, 26 days are incompatible with the exact rate sum; 10 is too small (too fast). Common Pitfalls: Forgetting to divide the summed pairwise rates by 2; arithmetic errors in fractional addition. Final Answer: 16 days

Question 5

A and B can finish a job in 12 days, B and C in 15 days, and C and A in 20 days. How many days would A alone take to complete the job?

Accepted Answer

Introduction / Context: With pairwise times, we can solve for individual rates. One reliable approach is to use the identity r(A) = [(A+B) + (A+C) − (B+C)] / 2 in rate form. Given Data / Assumptions: r(A)+r(B) = 1/12. r(B)+r(C) = 1/15. r(C)+r(A) = 1/20. Concept / Approach: Use r(A) = [ (r(A)+r(B)) + (r(A)+r(C)) − (r(B)+r(C)) ] / 2 and then invert to get A’s time. Step-by-Step Solution: r(A) = [1/12 + 1/20 − 1/15] / 2. Compute with denominator 60: 1/12=5/60, 1/20=3/60, 1/15=4/60. Numerator = (5/60 + 3/60 − 4/60) = 4/60 = 1/15. Divide by 2 ⇒ r(A) = (1/15)/2 = 1/30 per day. Hence A’s time alone = 30 days. Verification / Alternative check: Sum of pairwise rates = 1/12 + 1/15 + 1/20 = 0.2; half is 0.1 ⇒ total rate of A+B+C = 1/10. Then B+C = 1/15 ⇒ A = 1/10 − 1/15 = 1/30 (consistent). Why Other Options Are Wrong: 15 2/3, 24, 4, 20 days do not match the solved individual rate for A. Common Pitfalls: Forgetting to divide the adjusted sum by 2; mixing up which pair to subtract. Final Answer: 30 days

Question 6

A can do a job in 30 days and B can do the same job in 40 days. How many days will they take to finish the job when working together?

Accepted Answer

Introduction / Context: When two workers combine, their rates add. Convert individual times to rates, add, and invert to get the combined time. Given Data / Assumptions: A alone = 30 days ⇒ r(A) = 1/30 per day. B alone = 40 days ⇒ r(B) = 1/40 per day. Concept / Approach: Combined rate r = 1/30 + 1/40. Combined time T = 1 / r. Step-by-Step Solution: 1/30 + 1/40 = (4 + 3) / 120 = 7/120. T = 1 / (7/120) = 120/7 = 17 1/7 days. Verification / Alternative check: 17 1/7 × 7/120 = 1, confirming correctness. Why Other Options Are Wrong: 70, 42 3/4, 27 1/7, 24 days are inconsistent with the exact combined-rate inversion. Common Pitfalls: Averaging times (35 days) instead of adding rates; arithmetic slips in fraction handling. Final Answer: 17 1/7 days

Question 7

A can finish one-third (1/3) of a job in 5 days, while B can finish two-fifths (2/5) of the job in 10 days. In how many days can A and B together complete the entire job?

Accepted Answer

Introduction / Context: This problem gives partial completion benchmarks. Convert each to a full-job time or directly to daily rates, then add to get the joint rate and invert for total time. Given Data / Assumptions: A completes 1/3 in 5 days ⇒ daily rate r(A) = (1/3)/5 = 1/15. B completes 2/5 in 10 days ⇒ daily rate r(B) = (2/5)/10 = 1/25. Concept / Approach: Combined daily rate r = r(A) + r(B) = 1/15 + 1/25. Total time = 1 / r. Step-by-Step Solution: 1/15 + 1/25 = (5 + 3)/75 = 8/75. Total time = 1 / (8/75) = 75/8 = 9.375 days = 9 3/8 days. Verification / Alternative check: Decimal verification: 9.375 * (8/75) = 1, so the calculation is exact. Why Other Options Are Wrong: 7 3/4, 8 4/5, 10 days do not match the sum-of-rates inversion; 9 days is close but not exact. Common Pitfalls: Treating partial-job times as direct times instead of converting to rates; missing fraction simplifications. Final Answer: 9 3/8 days

Question 8

A can complete a job in 20 days while B can complete it in 12 days. If B works alone for 9 days and then A completes the remaining work alone, how many days does A take to finish the remainder?

Accepted Answer

Introduction / Context: This question mixes sequential work. We compute the fraction completed by B first, then the remaining fraction for A and divide by A’s rate to find the time required. Given Data / Assumptions: A alone = 20 days ⇒ r(A) = 1/20 per day. B alone = 12 days ⇒ r(B) = 1/12 per day. B works for 9 days first. Concept / Approach: Completed by B = 9 * (1/12) = 3/4. Remaining = 1 − 3/4 = 1/4. A’s daily rate is 1/20, so time = (remaining) / r(A). Step-by-Step Solution: Work done by B: 9/12 = 3/4. Remaining work: 1/4. A’s time = (1/4) / (1/20) = 5 days. Verification / Alternative check: Total time = 9 + 5 = 14 days; combined output matches the full job (3/4 + 1/4). Why Other Options Are Wrong: 3, 4, 7, 11 days do not match the exact remaining fraction and A’s rate. Common Pitfalls: Subtracting times rather than fractions of work; forgetting to compute the remaining fraction before dividing by A’s rate. Final Answer: 5 days

Question 9

A and B together can finish a work in 8 days. If A alone can finish it in 12 days, then how many days will B alone need to finish the work?

Accepted Answer

Introduction / Context: With the combined time and one individual’s time available, we subtract rates to find the other individual’s time. This is a standard rate subtraction technique. Given Data / Assumptions: A + B = 8 days ⇒ r(A+B) = 1/8 per day. A alone = 12 days ⇒ r(A) = 1/12 per day. Concept / Approach: r(B) = r(A+B) − r(A) = 1/8 − 1/12. Then B’s time = 1 / r(B). Step-by-Step Solution: 1/8 − 1/12 = (3 − 2)/24 = 1/24. Therefore, B’s time = 1 / (1/24) = 24 days. Verification / Alternative check: 1/12 + 1/24 = 1/8; hence A and B together take 8 days as given. Why Other Options Are Wrong: 12, 18, 20, 28 days do not produce the given combined time when paired with A’s 12-day rate. Common Pitfalls: Adding times instead of rates; miscomputing the common denominator when subtracting fractions. Final Answer: 24 days

Question 10

Rohan can finish a piece of work in 8 hours, while Sunil can finish it in 4 hours. If they work together, how much time will they take to complete the work?

Accepted Answer

Introduction / Context: This is a classic two-person work problem. The combined work rate is the sum of individual rates; the total time is the reciprocal of that sum. Given Data / Assumptions: Rohan alone = 8 hours ⇒ r(R) = 1/8 per hour. Sunil alone = 4 hours ⇒ r(S) = 1/4 per hour. Concept / Approach: Combined rate r = 1/8 + 1/4 = 3/8 per hour. Time together = 1 / r = 8/3 hours = 2 2/3 hours. Step-by-Step Solution: r(R+S) = 1/8 + 1/4 = 3/8 per hour. Time = 1 / (3/8) = 8/3 hours = 2 hours 40 minutes. Verification / Alternative check: In 2 2/3 hours, work done = (3/8) * (8/3) = 1 full job, confirming correctness. Why Other Options Are Wrong: 3 hours (too slow), 2 hours (too fast), 3 1/3 hours (too slow), 2 1/4 hours (too fast). Only 2 2/3 hours satisfies the exact rate sum inversion. Common Pitfalls: Averaging times instead of adding rates; arithmetic mistakes when converting 8/3 hours to hours and minutes. Final Answer: 2 2/3 hours

Question 11

A can do a piece of work in 12 days. B is 60% more efficient than A (i.e., B’s daily work rate is 1.6 times A’s rate). How many days will B alone take to finish the same work?

Accepted Answer

Introduction / Context: Efficiency comparisons directly scale time because time = work / rate. If one person is 60% more efficient, their rate is multiplied by 1.6, so their time is divided by 1.6 for the same job. Given Data / Assumptions: A’s time = 12 days ⇒ r(A) = 1/12 per day. B is 60% more efficient ⇒ r(B) = 1.6 * r(A). Concept / Approach: B’s time = A’s time / 1.6 = 12 / 1.6. Step-by-Step Solution: r(A) = 1/12; r(B) = 1.6 * (1/12) = 1/7.5 per day. Therefore, B’s time = 7.5 days = 7 1/2 days. Verification / Alternative check: Check: r(B) * 7.5 = (1.6/12) * 7.5 = 1 (complete job). Works out. Why Other Options Are Wrong: 6, 6 1/4, 8, 7 days do not equal 12 / 1.6 exactly. Common Pitfalls: Adding 60% to the time instead of adjusting the rate; confusing “more efficient” with “takes more time.” Final Answer: 7 1/2

Question 12

Time-and-Work basics, combined work rate: Worker A can finish a job in 12 days and worker B can finish the same job in 15 days. If A and B work together at their constant daily rates, how much time (in days) will they take to complete the entire wor…

Accepted Answer

Introduction / Context: This question checks your understanding of the fundamental “work = rate * time” idea used in Time and Work problems. When two workers collaborate, their rates add directly, and the combined time is computed from the sum of their individual daily work rates. Given Data / Assumptions: A alone finishes in 12 days ⇒ rate_A = 1/12 job per day. B alone finishes in 15 days ⇒ rate_B = 1/15 job per day. Both work together at constant rates until the whole job is completed. Concept / Approach: The combined daily rate is the sum of individual rates. If R is the total daily rate, then time T to finish one full job is T = 1 / R. Always keep units consistent: here, all times are in days and rates are jobs per day. Step-by-Step Solution: rate_A = 1/12rate_B = 1/15Combined rate R = 1/12 + 1/15 = (5 + 4)/60 = 9/60 = 3/20 job/dayTime T = 1 / R = 1 / (3/20) = 20/3 days = 6 2/3 days Verification / Alternative check: In 6 2/3 days, the pair completes (3/20) * (20/3) = 1 job. Any deviation (for example, 6 days or 8 days) would not satisfy R * T = 1. Why Other Options Are Wrong: 8 days: too long; at rate 3/20, that yields only 1.2 jobs? No—8*(3/20)=1.2 is more than one; 8 is inconsistent with the computed exact time. 10 1/15 days: not derived from rates; it overestimates time. 6 days: too short since 6*(3/20)=0.9 job. Common Pitfalls: Adding times instead of rates. Times never add directly; rates do. Arithmetic slip when converting to a mixed fraction. Final Answer: 6 2/3 days

Question 13

Sum of rates method, two workers: A can finish a job in 14 days, while B can finish it in 21 days. If both A and B work together at their constant rates, in how many days will they complete the entire work?

Accepted Answer

Introduction / Context: When two workers collaborate, their individual work rates add up. The total time to complete one whole job equals 1 divided by the combined rate. This problem reinforces that principle with clean numbers. Given Data / Assumptions: A alone: 14 days ⇒ rate_A = 1/14 job/day. B alone: 21 days ⇒ rate_B = 1/21 job/day. They work together from start to finish. Concept / Approach: Combined rate R = rate_A + rate_B. Time T = 1/R. Keep fractions precise to avoid rounding mistakes; convert to decimal at the end if needed. Step-by-Step Solution: rate_A = 1/14rate_B = 1/21R = 1/14 + 1/21 = (3 + 2)/42 = 5/42 job/dayT = 1 / (5/42) = 42/5 = 8.4 days Verification / Alternative check: Check work done in 8.4 days: 8.4 * (5/42) = 8.4 * 0.119047… = 1 job (exact since 42/5 * 5/42 = 1). Why Other Options Are Wrong: 10.5: equals A’s half-time notionally, not a valid combined time. 8 and 9: rounded guesses not consistent with exact 42/5. Common Pitfalls: Adding times instead of rates. Arithmetic error in LCM of 14 and 21 (LCM is 42). Final Answer: 8.4

Question 14

Efficiency comparison: A alone can do a job in 24 days. Worker B is 60% more efficient than A. How many days will B alone take to finish the same job?

Accepted Answer

Introduction / Context: This tests efficiency-to-time conversion. If B is more efficient than A, B’s time is proportionally lower because time is inversely proportional to efficiency for the same amount of work. Given Data / Assumptions: A’s time = 24 days ⇒ rate_A = 1/24 job/day. B is 60% more efficient than A ⇒ rate_B = 1.60 * rate_A. Concept / Approach: If efficiency increases by k%, multiply the base rate by (1 + k/100). Time = 1 / rate. So B’s time = A’s time / 1.60. Step-by-Step Solution: rate_A = 1/24rate_B = 1.6 * (1/24) = 1/15Time_B = 1 / (1/15) = 15 days Verification / Alternative check: Compare: 24 vs 15. A 60% boost in rate is a 37.5% reduction in time (since 9/24 = 37.5%), consistent with 24 → 15. Why Other Options Are Wrong: 12 and 10: too optimistic; imply even higher efficiency. 9.6: corresponds to 150% higher efficiency, not 60%. Common Pitfalls: Subtracting 60% from 24 (i.e., 24 − 60% of 24) which is wrong; time is not reduced linearly by the efficiency percentage. Final Answer: 15

Question 15

Relative efficiency and combined time: A is twice as efficient as B (i.e., A’s daily work rate is 2 times B’s). Together they finish a job in 14 days. In how many days can A alone finish the job?

Accepted Answer

Introduction / Context: This problem uses efficiency ratios. If A is twice as efficient as B, then A and B’s rates are in the ratio 2:1. The combined rate and total time are given, allowing us to isolate A’s time. Given Data / Assumptions: A : B (rates) = 2 : 1. Together they complete the job in 14 days. Concept / Approach: Let B’s rate be r; then A’s rate is 2r. Combined rate is 3r. If one full job requires time T with combined rate, then T = 1 / (3r). Since T = 14, we get r and then A’s time = 1 / (2r). Step-by-Step Solution: 3r = 1/14 ⇒ r = 1/42A’s rate = 2r = 2/42 = 1/21A’s time alone = 1 / (1/21) = 21 days Verification / Alternative check: Check: A+B combined rate = 1/21 + 1/42 = 3/42 = 1/14, so 14 days is consistent. Why Other Options Are Wrong: 18, 20, 24 are not consistent with the 2:1 efficiency ratio and 14-day combined time. Common Pitfalls: Using time ratios directly (they are inverse of efficiency ratios). Final Answer: 21

Question 16

Inverse relation of efficiency and time: Ajit is 3 times as efficient as Bablu. What is the ratio of the number of days required by Ajit and Bablu, respectively, to finish the job working alone?

Accepted Answer

Introduction / Context: This tests the inverse relationship between efficiency and time. If Ajit is faster (more efficient), he takes fewer days. The product (efficiency * time) needed for one job is constant (equal to 1 job). Given Data / Assumptions: Efficiency_Ajit = 3 * Efficiency_Bablu. Each works alone at a constant rate. Concept / Approach: Let Bablu’s time be T. Since Ajit is 3 times as efficient, Ajit’s time is T/3. Therefore, (Ajit days) : (Bablu days) = (T/3) : T = 1 : 3. Step-by-Step Solution: If rate_B = r, then rate_A = 3r.Time_B = 1/r, Time_A = 1/(3r) = (1/3)*(1/r).Thus, Time_A : Time_B = 1/3 : 1 = 1 : 3. Verification / Alternative check: Pick numbers: if Bablu needs 30 days, Ajit needs 10 days → 10:30 = 1:3, matching the reasoning. Why Other Options Are Wrong: 3:1 and 6:3 invert the inverse relationship; those are efficiency ratios, not time ratios. 3:6 simplifies to 1:2, still incorrect. Common Pitfalls: Confusing efficiency ratio with time ratio. They are reciprocals. Final Answer: 1 : 3

Question 17

Clarifying “times more efficient” and days ratio: Assume X works at a rate five times that of Y (interpreting “4 times more efficient” as X is 5 times as efficient as Y). What is the ratio of the number of days taken by X and Y, respectively, to do …

Accepted Answer

Introduction / Context: The phrase “4 times more efficient” is ambiguous. In many aptitude settings it is intended to mean “4 times as efficient” (i.e., 4X). However, strictly parsed English can interpret “4 times more than Y” as X = Y + 4Y = 5Y. Under the Recovery-First policy, we make the minimal clarification that renders one of the provided options correct by interpreting X = 5Y so the question is solvable with the given choices. Given Data / Assumptions: Take rate_X = 5 * rate_Y (clarified interpretation). Each works alone on the same job. Concept / Approach: Time is inversely proportional to rate. Therefore, the ratio of days (X : Y) equals the inverse of the rate ratio (Y : X). Step-by-Step Solution: rate_X : rate_Y = 5 : 1days_X : days_Y = 1/5 : 1 = 1 : 5 Verification / Alternative check: Pick a total work of 1 job. If rate_Y = 1 unit/day ⇒ time_Y = 1 day to do 1 unit (toy illustration). If rate_X = 5 units/day ⇒ time_X = 1/5 day. The ratio of times is 1/5 : 1 = 1 : 5. Why Other Options Are Wrong: 5 : 1 and 8 : 1 are rate-style answers, not time ratios. 6 : 8 is unrelated to the 5:1 assumption. Common Pitfalls: Mistaking “times more efficient” for a clean multiplicative factor without clarifying whether it is +4Y or ×4. Final Answer: 1 : 5

Question 18

Inferring a second worker’s rate and then combining: Sonu can complete a job in 20 days. He works alone for some days until 25% of the job is finished. Abhijeet then works alone and finishes the remaining work in 10 days. If Sonu and Abhijeet work t…

Accepted Answer

Introduction / Context: This problem involves first deducing Abhijeet’s solo rate from the information about the remaining work and then computing the combined time if both worked together throughout. It tests rate inference and combined-rate application. Given Data / Assumptions: Sonu’s time alone = 20 days ⇒ rate_S = 1/20 job/day. When Sonu stops, 25% is done ⇒ 75% remains. Abhijeet finishes the remaining 75% in 10 days ⇒ rate_A = 0.75 / 10 = 0.075 job/day. Concept / Approach: Once both rates are known, the combined rate is the sum. The total time for one job at the combined rate is T = 1 / (rate_S + rate_A). Step-by-Step Solution: rate_S = 1/20 = 0.05rate_A = 0.75 / 10 = 0.075Combined rate = 0.05 + 0.075 = 0.125 job/dayTogether time T = 1 / 0.125 = 8 days Verification / Alternative check: Check: In 8 days at 0.125 job/day, they complete exactly 1 job. Also, Abhijeet’s inferred full-time to complete alone would be 1 / 0.075 ≈ 13.33 days, which is consistent with finishing 75% in 10 days. Why Other Options Are Wrong: 6 and 10 days correspond to incorrect combined rates. 12 days is too slow compared to the derived 8 days. Common Pitfalls: Mistaking 25% as the remaining work instead of the completed part. Forgetting that rates add when people work together. Final Answer: 8

Question 19

Three taps filling a tank with one tap closed later: Taps A, B, and C together can fill a tank in 6 hours. After all three run for 2 hours, tap C is closed and the remaining part is filled by A and B in 8 more hours. In how many hours can C alone fi…

Accepted Answer

Introduction / Context: Classic pipes-and-cisterns setup: total rate is given, then one pipe is turned off. We use the initial joint work to find what remains, infer A+B rate from the second phase, and subtract from total to isolate C’s rate. Given Data / Assumptions: A + B + C together fill in 6 h ⇒ combined rate = 1/6 tank/h. All three run for 2 h ⇒ filled = 2 * (1/6) = 1/3 of the tank. Remaining = 2/3 of the tank, filled in 8 h by A + B only. Concept / Approach: From phase two: (A + B) * 8 = 2/3 ⇒ A + B = 1/12. Since A + B + C = 1/6, we get C = (1/6 − 1/12) = 1/12 tank/h. Time of C alone is reciprocal of its rate. Step-by-Step Solution: Total rate (A+B+C) = 1/6In 2 h, work done = 2/6 = 1/3Remaining = 2/3 = (A+B)*8 ⇒ A+B = (2/3)/8 = 1/12Thus C = 1/6 − 1/12 = 1/12Time for C alone = 1 / (1/12) = 12 h Verification / Alternative check: Reconstruct: Phase 1 adds 1/3; Phase 2 with A+B at 1/12 for 8 h adds 2/3 → total 1 tank, consistent. Why Other Options Are Wrong: 16 h, 14 h, 18 h contradict the exact subtraction of rates and second-phase computation. Common Pitfalls: Mistaking the remaining fraction after 2 h. Adding or subtracting times instead of rates. Final Answer: 12 h

Question 20

Working on alternate days: Alen can do a job in 21 days and Border in 42 days working alone. If they work on alternate days starting with Alen (day 1), in how many days will the work be completed?

Accepted Answer

Introduction / Context: Alternate-day problems are solved by computing the work done in a 2-day cycle and then scaling. Starting worker matters if the total is not a multiple of the cycle output, but this pair divides nicely. Given Data / Assumptions: Alen alone: 21 days ⇒ rate_A = 1/21. Border alone: 42 days ⇒ rate_B = 1/42. They alternate days starting with Alen. Concept / Approach: Compute 2-day work = 1/21 + 1/42 = 3/42 = 1/14 of the job. One full job needs 14 such 2-day cycles if it divides exactly. Step-by-Step Solution: 2-day output = 1/21 + 1/42 = 1/14To complete 1 job: need 14 cycles × 2 days = 28 days Verification / Alternative check: After 28 days, the total done is 14 * (1/14) = 1 job. No fractional day is needed because the cycle output divides the job exactly. Why Other Options Are Wrong: 14: would require 1/14 per day, but they achieve 1/14 in two days, not one. 42 and 35: are longer than the exact computed 28 days. Common Pitfalls: Assuming linear averaging of times instead of cycle-based aggregation. Final Answer: 28

Time and Work Questions