Question 1

Man-days scaling to a fraction of a day: 10 men can build a wall in 8 days. How many men are required to complete the same work in half a day (assume identical efficiency)?

Accepted Answer

Introduction / Context: This uses the man-days concept with a very short target time. If the total man-days are fixed for a given job, reducing the days to a fraction requires increasing the number of men proportionally to keep the product constant. Given Data / Assumptions: 10 men * 8 days = fixed work. All men work at the same rate. Target completion time = 0.5 day (half a day). Concept / Approach: Total man-days required = 10 * 8 = 80. Required men = total man-days / target days = 80 / 0.5. Step-by-Step Solution: Total man-days = 80. Men needed in 0.5 day = 80 / 0.5 = 160. Verification / Alternative check: Check proportionality: target time is 1/16 of 8 days; thus men must be 16 times 10, i.e., 160 men. Why Other Options Are Wrong: 80, 100, 120 do not satisfy 80 man-days when multiplied by 0.5 day. Common Pitfalls: Misreading “half a day” as “half the days.” Here it explicitly means 0.5 day, not 4 days. Final Answer: 160

Question 2

Mixed workforce (men and women): 3 men can finish a job in 6 days and 5 women can finish the same job in 18 days. If 4 men and 10 women work together, how many days will they require to finish the job?

Accepted Answer

Introduction / Context: We combine different worker categories with different efficiencies. Convert both groups into daily rates from their solo completion info, add the rates for the mixed team, and then invert to get total days needed. Given Data / Assumptions: 3 men in 6 days ⇒ 3m * 6 = 1 ⇒ m = 1/18 job/day. 5 women in 18 days ⇒ 5w * 18 = 1 ⇒ w = 1/90 job/day. Team = 4 men + 10 women. Concept / Approach: Team rate = 4m + 10w. Then days = 1 / (team rate). Each rate is constant and additive since they work simultaneously on the same job. Step-by-Step Solution: m = 1/18; w = 1/90. Team rate = 4*(1/18) + 10*(1/90) = 4/18 + 10/90 = 2/9 + 1/9 = 1/3. Days = 1 / (1/3) = 3 days. Verification / Alternative check: Note that 1 man = 5 women in productivity (since 1/18 : 1/90 = 5:1). The team equals 4 men + 10 women = 4 + 2 man-equivalents = 6 men ⇒ 6 men at 1/18 each give 6/18 = 1/3 job/day ⇒ 3 days. Why Other Options Are Wrong: 2, 4, or 5 days contradict the calculated combined rate. Common Pitfalls: Averaging days instead of rates; you must convert to daily rates before summing across categories. Final Answer: 3 days

Question 3

Men and children together: 3 men can do a work in 18 days; 6 children can do the same work in 18 days. How many days will 4 men and 4 children together need to finish the work?

Accepted Answer

Introduction / Context: This is another mixed-rate problem. First find the relative productivity between a man and a child, then sum the rates for the combined group and invert to get the total time required. Given Data / Assumptions: 3 men * 18 days = 1 job ⇒ man rate m = 1/(3*18) = 1/54 job/day per man. 6 children * 18 days = 1 job ⇒ child rate c = 1/(6*18) = 1/108 job/day per child. Team = 4 men + 4 children. Concept / Approach: Team rate = 4m + 4c. Compute this numeric rate and then compute days = 1 / (team rate). Equivalently, note that 1 man = 2 children since 1/54 is twice 1/108. Step-by-Step Solution: m = 1/54; c = 1/108 ⇒ 1 man = 2 children. Team rate = 4*(1/54) + 4*(1/108) = 4/54 + 4/108 = 2/27 + 1/27 = 3/27 = 1/9. Days = 1 / (1/9) = 9. Verification / Alternative check: Convert to man-equivalents: 4 men + 4 children = 4 + 2 = 6 man-equivalents; total rate = 6*(1/54) = 1/9 job/day ⇒ 9 days. Why Other Options Are Wrong: 6, 10, or 12 days contradict the derived combined rate of 1/9 job/day. Common Pitfalls: Adding days instead of rates, or assuming equal productivity across men and children without computing it. Final Answer: 9

Question 4

Three-person collaboration: P can do a work in 12 days, Q alone in 8 days, and with the help of R they finish in 4 days. How many days would R alone take to complete the work?

Accepted Answer

Introduction / Context: We are given two solo rates and the combined rate with a third person. Subtract the known solo rates from the team rate to isolate R’s rate, then invert to get R’s solo time for the complete job. Given Data / Assumptions: P’s time = 12 days ⇒ rate_P = 1/12. Q’s time = 8 days ⇒ rate_Q = 1/8. (P + Q + R) time = 4 days ⇒ joint rate = 1/4. Concept / Approach: rate_R = (1/4) − (1/12) − (1/8). Compute numerically and invert for R’s time alone. Step-by-Step Solution: 1/4 − 1/12 − 1/8 = (6 − 2 − 3)/24 = 1/24. Therefore, R alone takes 24 days. Verification / Alternative check: Check by addition: 1/12 + 1/8 + 1/24 = 2/24 + 3/24 + 1/24 = 6/24 = 1/4, consistent with 4 days together. Why Other Options Are Wrong: 25 or 34 are arbitrary; 14 is too fast and fails the rate sum check. Common Pitfalls: Arithmetic with fractions; always use a common denominator to avoid mistakes. Final Answer: 24 days

Question 5

Staggered start in work: A alone can finish a job in 15 days, and B alone can do it in 10 days. A starts the work and B joins after 5 days. For how many total days did the work last until completion?

Accepted Answer

Introduction / Context: This is a partial-duration collaboration problem. A works alone initially, then B joins. We track the fraction of work completed by A in the first phase and then compute the time for the remainder at the combined rate in the second phase. Given Data / Assumptions: A’s time = 15 days ⇒ rate_A = 1/15. B’s time = 10 days ⇒ rate_B = 1/10. A works alone for 5 days, then A and B work together until completion. Concept / Approach: Work done in first 5 days = 5 * (1/15) = 1/3. Remaining work = 2/3. Combined rate = 1/15 + 1/10 = 1/6 job/day. Time for remainder = (2/3) / (1/6). Add the initial 5 days to get total duration. Step-by-Step Solution: Initial work by A in 5 days = 5/15 = 1/3. Remaining = 1 − 1/3 = 2/3. Combined rate = 1/15 + 1/10 = (2 + 3)/30 = 1/6. Time for remainder = (2/3) / (1/6) = (2/3)*6 = 4 days. Total duration = 5 + 4 = 9 days. Verification / Alternative check: Rate check: In the last 4 days at 1/6 per day, they do 4/6 = 2/3, which matches the remaining portion. Why Other Options Are Wrong: 8 or 5 days do not account for the correct split; 4 days is only the second phase, not the total. Common Pitfalls: Forgetting to add the initial solo days to the subsequent joint days; mixing up fractions when switching phases. Final Answer: 9

Question 6

Efficiency comparison: A does 20% less work than B (i.e., A’s rate is 20% lower). If A can complete the job in 7.5 hours, in how many hours can B complete the same job?

Accepted Answer

Introduction / Context: When one worker is a certain percentage less efficient than another, their times are inversely related to their efficiencies. A being 20% less efficient than B means B is faster. We use proportional reasoning to compute B’s time from A’s time. Given Data / Assumptions: A's rate = 80% of B's rate (since 20% less). A’s time = 7.5 hours for the full job. Work amount is the same for both (1 job). Concept / Approach: Time is inversely proportional to rate. If r_A = 0.8 * r_B, then T_A = (1 / r_A) and T_B = (1 / r_B) = (1 / (r_A / 0.8)) = 0.8 * T_A. Thus we scale A’s time by 0.8 to get B’s time. Step-by-Step Solution: T_B = 0.8 * T_A = 0.8 * 7.5 = 6 hours. Verification / Alternative check: Relative rates: If B's rate = 1 unit/hour, A's rate = 0.8 unit/hour. Times are 1 and 1/0.8 = 1.25 units of time; ratio T_A : T_B = 1.25 : 1 = 5 : 4 ⇒ T_B = 4/5 * 7.5 = 6 hours. Why Other Options Are Wrong: 4 h is too fast; 8 h and 10 h are too slow compared with A’s 7.5 h for a worker who is more efficient. Common Pitfalls: Treating “20% less work” as subtracting time rather than scaling rate; the correct relation is via inverse proportionality of time and rate. Final Answer: 6 h

Question 7

Relative efficiency increase: X can complete a work in 16 days. If Y’s efficiency is 60% more than X’s efficiency, in how many days can Y complete the same work?

Accepted Answer

Introduction / Context: Efficiency and time are inversely proportional. “60% more efficient” means the rate is multiplied by 1.6. Therefore, the time to complete a fixed job is divided by 1.6. We apply this directly to X’s 16-day benchmark to find Y’s days. Given Data / Assumptions: X’s time = 16 days ⇒ baseline rate r_X. Y’s rate = 1.6 * r_X (60% more efficient). Job size is the same for both. Concept / Approach: T_Y = T_X / 1.6. This follows from time = work / rate, with work held constant and rate scaled by 1.6. Step-by-Step Solution: T_Y = 16 / 1.6 = 10 days. Verification / Alternative check: If r_X = 1/16 job/day, then r_Y = 1.6/16 = 0.1 job/day ⇒ 1 / 0.1 = 10 days, consistent. Why Other Options Are Wrong: 12, 25, 30 days do not correspond to a 60% increase in rate over a 16-day baseline. Common Pitfalls: Adding 60% to the time instead of the rate, or subtracting 60%—remember the inverse relation between time and efficiency. Final Answer: 10 days

Question 8

Men and women together with partial information: 2 men and 3 women finish 25% of a job in 4 days. Also, 6 men and 14 women finish the whole job in 5 days. In how many days will 20 women finish the entire work?

Accepted Answer

Introduction / Context: This problem provides two linear equations about the combined rates of men and women, one for a quarter of the job and one for the full job. We solve the system to find an individual woman’s daily rate and then scale up to 20 women to determine completion time. Given Data / Assumptions: (2m + 3w) * 4 days = 0.25 job ⇒ 8m + 12w = 0.25. (6m + 14w) * 5 days = 1 job ⇒ 30m + 70w = 1. m = man’s daily rate; w = woman’s daily rate; rates are constant. Concept / Approach: Reduce the equations and solve simultaneously for m and w. Then compute the collective rate of 20 women (20w) and invert to find days for the whole job. Step-by-Step Solution: From 8m + 12w = 0.25 ⇒ divide by 4 ⇒ 2m + 3w = 0.0625. From 30m + 70w = 1 ⇒ divide by 10 ⇒ 3m + 7w = 0.1. Multiply the first by 3: 6m + 9w = 0.1875. Multiply the second by 2: 6m + 14w = 0.2. Subtract: (6m + 14w) − (6m + 9w) = 0.2 − 0.1875 ⇒ 5w = 0.0125 ⇒ w = 0.0025. Rate of 20 women = 20 * 0.0025 = 0.05 job/day. Days for 20 women = 1 / 0.05 = 20 days. Verification / Alternative check: Quick check with w = 0.0025 back in the equations gives consistent totals; m can be found but is not needed for the final answer. Why Other Options Are Wrong: 25 and 24 assume different rates; 88 is not supported by the simultaneous equations. Common Pitfalls: Arithmetic slips with decimals or not reducing equations before solving. Keep fractions/decimals aligned when eliminating variables. Final Answer: 20

Question 9

Determine a woman’s solo time from a mixed team: 10 men and 15 women finish a work in 6 days. One man alone can finish the same work in 100 days. In how many days can one woman alone finish the work?

Accepted Answer

Introduction / Context: We are given the team time and one man’s solo time. From the team rate equation, we can isolate the woman’s rate and then invert to find her solo completion time. This is a straightforward linear rate problem once written correctly. Given Data / Assumptions: Total job = 1. 1 man’s time = 100 days ⇒ man’s rate m = 1/100. (10 men + 15 women) complete in 6 days ⇒ team rate = 1/6. Concept / Approach: Team rate = 10m + 15w = 1/6. Substitute m = 1/100 and solve for w (woman’s rate). Then woman’s solo time is 1 / w days. Step-by-Step Solution: 10m + 15w = 1/6 ⇒ 10*(1/100) + 15w = 1/6. 0.1 + 15w = 0.166666... ⇒ 15w = 0.066666... = 1/15. Therefore, w = (1/15)/15 = 1/225. One woman’s time = 1 / (1/225) = 225 days. Verification / Alternative check: Plugging back: 10*(1/100) + 15*(1/225) = 0.1 + 0.066666... = 0.166666... = 1/6, consistent. Why Other Options Are Wrong: 125, 150, 90 days do not satisfy the team equation when substituted. Common Pitfalls: Rounding errors with repeating decimals; treat 1/6 exactly when possible to avoid drift. Final Answer: 225 days

Question 10

Share in contract work: A, B and C contract to complete a work for Rs. 550. Together A and B are supposed to do 7/11 of the work. What should be C’s share of the payment?

Accepted Answer

Introduction / Context: Payments in such problems are proportional to the share of work done. If A and B together are responsible for a known fraction of the job, the remainder belongs to C. Multiply C’s fraction by the total contract value to find C’s monetary share. Given Data / Assumptions: Total contract value = Rs. 550. Work shares are proportional to payments. A + B share of work = 7/11. Concept / Approach: C’s work fraction = 1 − 7/11 = 4/11. Therefore, C’s payment = (4/11) * 550. Compute this product directly. Step-by-Step Solution: C’s fraction = 1 − 7/11 = 4/11. C’s share = 550 * (4/11) = 50 * 4 = Rs. 200. Verification / Alternative check: A + B would then receive 7/11 * 550 = Rs. 350; adding C’s Rs. 200 returns Rs. 550 total. Why Other Options Are Wrong: Rs. 1831/3 and Rs. 300 or Rs. 400 do not correspond to the 4/11 fraction of Rs. 550. Common Pitfalls: Misinterpreting “supposed to do 7/11” as money instead of work; here payment follows actual work share. Final Answer: Rs. 200

Question 11

Time and Work — Individual vs. Combined Rates A can complete the work alone in 6 days, and B can complete the same work alone in 3 days. If A and B work together from start to finish, in how many days will they complete the entire work?

Accepted Answer

Introduction / Context:This time-and-work question tests your ability to convert individual completion times into rates, add those rates for combined work, and then invert the sum to find the total time. It is a foundational technique used in aptitude tests and project-planning scenarios. Given Data / Assumptions: A alone finishes in 6 days. B alone finishes in 3 days. They both work together continuously at constant rates. Concept / Approach:Define one full job as 1 unit of work. The work rate of a person is 1/(their time). Combined work rate is the sum of individual rates. Time to finish = 1/(combined rate). Step-by-Step Solution:A's rate = 1/6 job per day.B's rate = 1/3 job per day.Combined rate = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2 job per day.Total time = 1 / (1/2) = 2 days. Verification / Alternative check:If they complete half the job per day, then after 2 days the entire job is done. This matches the computed time exactly. Why Other Options Are Wrong:3, 4, and 5 days imply slower combined rates than actually achieved. 6 days equals A's solo time and ignores B's contribution. Common Pitfalls:Adding times directly (e.g., 6 + 3) or averaging 6 and 3 is incorrect. You must add rates (reciprocals of times), not the times themselves. Final Answer:2 days

Question 12

Work Rates — Isolating One Worker's Time from Group Data Ram, Dilip, and Shekhar together complete a job in 20 days. Ram and Dilip together complete the same job in 30 days. How many days would Shekhar alone take to complete the job?

Accepted Answer

Introduction / Context:This problem focuses on separating one worker’s contribution from group performance. By converting times to rates and subtracting the pair’s rate from the trio’s rate, we can find Shekhar’s rate and hence his time alone. Given Data / Assumptions: (Ram + Dilip + Shekhar) time = 20 days. (Ram + Dilip) time = 30 days. Constant work rates throughout. Concept / Approach:Rate = 1/time. Let total work = 1 job. Then r_total = 1/20 and r_RD = 1/30. Shekhar's rate r_S = r_total − r_RD. Finally, time_S = 1/r_S. Step-by-Step Solution:r_total = 1/20 job/dayr_RD = 1/30 job/dayr_S = 1/20 − 1/30 = (3 − 2)/60 = 1/60 job/dayShekhar's time = 1 / (1/60) = 60 days Verification / Alternative check:In 60 days Shekhar does exactly 1 job. Group minus pair equals the single worker’s rate; arithmetic checks out. Why Other Options Are Wrong:62, 56, 50, and 40 days do not align with r_S = 1/60 derived from the rates difference. Common Pitfalls:Subtracting times instead of rates, or mixing up which figure represents the trio vs. the pair. Final Answer:60 days

Question 13

Three Workers with Different Efficiencies Sunil completes the work in 4 days, Dinesh in 6 days, and Ramesh works 1.5 times as fast as Sunil. If all three work together from the start, how many days are required to finish the work?

Accepted Answer

Introduction / Context:This problem features three different rates, including one given as a multiple of another's efficiency. We must convert all to daily work rates, add them, and invert to get the combined time. It highlights the importance of working with rates rather than times. Given Data / Assumptions: Sunil time = 4 days ⇒ rate = 1/4. Dinesh time = 6 days ⇒ rate = 1/6. Ramesh is 1.5 times as fast as Sunil ⇒ rate = 1.5*(1/4) = 3/8. All three work together without interruption. Concept / Approach:Sum the rates: r_total = r_Sunil + r_Dinesh + r_Ramesh. Then total time = 1 / r_total. Keep fractions exact to avoid rounding issues. Step-by-Step Solution:r_total = 1/4 + 1/6 + 3/8LCM 24: 1/4 = 6/24, 1/6 = 4/24, 3/8 = 9/24r_total = (6 + 4 + 9)/24 = 19/24 job/dayTime = 1 / (19/24) = 24/19 days ≈ 1.263 days Verification / Alternative check:Decimal check: 0.25 + 0.1667 + 0.375 = 0.7917 job/day; inverse ≈ 1.263 days, matching 24/19. Why Other Options Are Wrong:7/12, 15/12, and 15/7 do not equal 24/19. Hence the correct selection is “None of these.” Common Pitfalls:Using 1.5 days instead of 1.5 times rate; remember “times as fast” multiplies the rate, not the time. Final Answer:None of these

Question 14

Staggered Start — One Worker Joins Later Mahesh and Umesh can complete a job in 10 days and 15 days, respectively. Umesh works alone for the first 5 days, after which Mahesh also joins. In how many total days is the work completed?

Accepted Answer

Introduction / Context:When one worker starts and another joins later, split the timeline into phases and compute the partial work done in each phase using rates. Sum the completed parts to reach the full job. Given Data / Assumptions: Mahesh alone: 10 days ⇒ rate = 1/10. Umesh alone: 15 days ⇒ rate = 1/15. Phase 1: Umesh works 5 days alone. Phase 2: Both work together afterward. Concept / Approach:Compute work done in Phase 1, subtract from 1, and finish the remainder using the combined rate. Step-by-Step Solution:Phase 1 work by Umesh = 5*(1/15) = 1/3.Remaining work = 1 − 1/3 = 2/3.Combined rate (Mahesh + Umesh) = 1/10 + 1/15 = 1/6 job/day.Time for remaining = (2/3) / (1/6) = (2/3)*6 = 4 days.Total time = 5 + 4 = 9 days. Verification / Alternative check:Daily contributions in Phase 2 sum to 1/6; in 4 days they complete 4/6 = 2/3, exactly what was left. Why Other Options Are Wrong:7, 8, 10, or 11 days do not match the phased rate calculation. Common Pitfalls:Adding times directly or forgetting to subtract the work already done in Phase 1 before computing Phase 2 duration. Final Answer:9 days

Question 15

Two Workers — Partial Contribution Then Solo Finish A can do the work in 80 days. He works alone for 10 days, and then B alone finishes the remaining work in 42 days. If A and B worked together from the start, in how many days would they finish?

Accepted Answer

Introduction / Context:This question blends partial work and rate-finding. By using the given phases, we determine B’s solo rate and then add A’s rate to find a combined completion time. Given Data / Assumptions: A alone: 80 days ⇒ rate = 1/80. A works 10 days initially. B alone finishes in 42 days. Concept / Approach:Compute how much work A completes in 10 days. The remainder is done by B; from this we get B’s rate. Then add rates to get the together time. Step-by-Step Solution:Work done by A in 10 days = 10*(1/80) = 1/8.Remaining = 1 − 1/8 = 7/8.B completes 7/8 in 42 days ⇒ B's rate = (7/8)/42 = 1/48.Combined rate = 1/80 + 1/48 = (3 + 5)/240 = 8/240 = 1/30.Together time = 1 / (1/30) = 30 days. Verification / Alternative check:Check B's time alone: 1/48 implies 48 days per job; 7/8 of a job in 42 days fits. Why Other Options Are Wrong:25, 24, 35, and 40 do not match the computed combined rate of 1/30. Common Pitfalls:Using 42 as B’s full-time duration for a whole job without adjusting for the fractional workload. Final Answer:30 days

Question 16

Staggered Collaboration — B Joins After 10 Days A can complete a job in 25 days and B can complete it in 20 days. A starts alone and B joins after 10 days. What is the total duration of the work (in days)?

Accepted Answer

Introduction / Context:Another phased-work problem: one person starts, the second joins later. Compute the work done initially, then finish the rest at the combined rate. Convert fractional days to mixed fractions at the end for clarity. Given Data / Assumptions: A alone: 25 days ⇒ rate = 1/25. B alone: 20 days ⇒ rate = 1/20. A works alone for first 10 days. Concept / Approach:Work after 10 days by A is subtracted from the total. The remainder is completed at the combined rate (A + B). Step-by-Step Solution:Work by A in 10 days = 10*(1/25) = 2/5.Remaining = 1 − 2/5 = 3/5.Combined rate (A + B) = 1/25 + 1/20 = 9/100 per day.Time for remaining = (3/5) / (9/100) = (3/5)*(100/9) = 60/9 = 20/3 days = 6 2/3 days.Total time = 10 + 6 2/3 = 16 2/3 days. Verification / Alternative check:Decimal: 9/100 = 0.09 per day. Remaining 0.6/0.09 = 6.666... days, confirming the result. Why Other Options Are Wrong:Other durations do not satisfy the phased-rate arithmetic. Common Pitfalls:Adding times directly or treating B’s contribution as starting earlier than given. Final Answer:16 2/3 days

Question 17

Team Size Changes Midway 14 men can complete a work in 12 days. After 4 days, 2 more men join. How many additional days are needed to complete the remaining work?

Accepted Answer

Introduction / Context:Here, workforce changes partway through the project. The correct approach is to use man-days (men * days) to measure total work and calculate what remains after the first phase, adjusting for the new team size afterwards. Given Data / Assumptions: Total with 14 men in 12 days ⇒ total work = 14*12 = 168 man-days. First 4 days with 14 men ⇒ 14*4 = 56 man-days completed. Then 2 more join ⇒ 16 men continue. Concept / Approach:Remaining work (in man-days) divided by the new daily capacity (men per day) gives remaining days. Step-by-Step Solution:Total work = 168 man-days.Done in first phase = 56 man-days.Remaining = 168 − 56 = 112 man-days.With 16 men: days needed = 112 / 16 = 7 days. Verification / Alternative check:Performing the calculation in fractional jobs gives the same answer; the man-day approach is clean and direct here. Why Other Options Are Wrong:5, 6, 8, or 9 days are not consistent with 112 man-days divided by 16 men. Common Pitfalls:Not converting to man-days first or assuming proportionality without accounting for the first phase’s contribution. Final Answer:7 days

Question 18

Mid-Project Replacement and Net Team Size 12 men can finish a job in 9 days. After 3 days, 6 men join to replace 2 men (net change in team size). How many more days are needed to finish the remaining work?

Accepted Answer

Introduction / Context:The statement “6 men joined to replace 2 men” implies 2 left and 6 joined, so the new team size is 12 − 2 + 6 = 16. Use total man-days and phase-wise accounting to compute the remaining time with the new team size. Given Data / Assumptions: Total work with 12 men in 9 days ⇒ 12*9 = 108 man-days. First 3 days at 12 men ⇒ 36 man-days completed. After that, effective team size = 16 men. Concept / Approach:Remaining man-days divided by the new daily capacity (16) gives the remaining time. Step-by-Step Solution:Remaining work = 108 − 36 = 72 man-days.Days needed with 16 men = 72 / 16 = 4.5 days = 4 1/2 days. Verification / Alternative check:Fractional days are acceptable because the last day need not be whole; work is continuous. Why Other Options Are Wrong:2, 3, and 4 days are too few; 5 is too many relative to 72 man-days and 16 men. Common Pitfalls:Misreading “replace” as net zero change; the wording indicates 2 left and 6 joined, producing a net +4 men. Final Answer:4 1/2

Question 19

Three People Working Together A can do a job in 8 days, B can do it in 16 days, and C can do it in 80 days. If all three work together, how many days are needed to complete the work?

Accepted Answer

Introduction / Context:This is a straightforward combined-rate problem involving three workers. Convert each to a rate, add them, and invert to get the total time. Such questions appear frequently in aptitude tests. Given Data / Assumptions: A: 8 days ⇒ 1/8 per day. B: 16 days ⇒ 1/16 per day. C: 80 days ⇒ 1/80 per day. Concept / Approach:Combined rate r = 1/8 + 1/16 + 1/80. Time = 1/r. Use a common denominator to avoid errors. Step-by-Step Solution:Common denominator 80: 1/8 = 10/80, 1/16 = 5/80, 1/80 = 1/80.r = (10 + 5 + 1)/80 = 16/80 = 1/5 job/day.Time = 1 / (1/5) = 5 days. Verification / Alternative check:Average speed logic confirms that adding even a slow helper (C) still improves total rate modestly, not dramatically. Why Other Options Are Wrong:6 or more days imply a rate slower than 1/5; 8 2/3 and 20 2/5 are far off; 4 days would require a faster combined rate than available. Common Pitfalls:Adding times instead of rates or omitting the contribution of the slowest worker altogether. Final Answer:5

Question 20

Classic Pair-Work Problem A can do a piece of work in 10 days and B can do it in 15 days. If they work together from start to finish, in how many days will they complete the work?

Accepted Answer

Introduction / Context:This is a standard two-person time-and-work problem. The trick is to add the rates (reciprocals of the times) and invert to find the combined duration. Given Data / Assumptions: A: 10 days ⇒ 1/10 per day. B: 15 days ⇒ 1/15 per day. Concept / Approach:Combined rate r = 1/10 + 1/15 = (3 + 2)/30 = 5/30 = 1/6. Total time = 1/r = 6 days. Step-by-Step Solution:r = 1/10 + 1/15 = 1/6 job/dayTime = 1 / (1/6) = 6 days Verification / Alternative check:If they complete 1/6 per day together, in 6 days they finish the job, matching the calculation. Why Other Options Are Wrong:8, 9, 10, and 12 days are inconsistent with the derived combined rate of 1/6 per day. Common Pitfalls:Using the average of 10 and 15 instead of the reciprocal-sum method. Final Answer:6

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