Question 1

Typing work with an interruption: A report of 100 pages is to be typed by three typists. Speeds: A types 100 pages in 10 hours, B in 20 hours, and C in 25 hours. All start at 09:00 a.m. At 01:00 p.m. (after 4 hours) A stops. B and C continue and fin…

Accepted Answer

Introduction / Context:Translate times to page-per-hour speeds, compute pages typed before A leaves, then finish with the remaining two typists. Given Data / Assumptions: A: 100 pages/10 h = 10 pph. B: 100 pages/20 h = 5 pph. C: 100 pages/25 h = 4 pph. All start 09:00; A stops at 13:00. Concept / Approach:Pages done till 13:00 plus remaining pages divided by the combined B + C speed gives the additional time. Step-by-Step Solution:First 4 hours at combined 10 + 5 + 4 = 19 pph ⇒ 4 * 19 = 76 pages done.Remaining pages = 100 − 76 = 24 pages.B + C speed = 5 + 4 = 9 pph.Time to finish = 24 / 9 = 2 h 40 m.Finish time = 13:00 + 2:40 = 15:40 ⇒ 3:40 p.m. Verification / Alternative check:Compute in fractions: 24/9 = 8/3 h = 2 h 40 m, same result. Why Other Options Are Wrong:Other times add or subtract incorrect intervals or miscompute initial pages. Common Pitfalls:Using total pages typed by A beyond 13:00 by mistake or averaging speeds. Final Answer:3:40 p.m.

Question 2

Men vs. boys productivity equivalence: 15 men can complete a work in 10 days, while 20 boys can complete the same work in 15 days. If 10 men and 10 boys work together, how many days will they take to finish the work?

Accepted Answer

Introduction / Context:We first equate total job sizes to deduce the relative productivity of a boy vs a man, then combine rates for the mixed team. Given Data / Assumptions: 15 men × 10 days = 150 man-days = job size. 20 boys × 15 days = 300 boy-days = same job. Concept / Approach:From equality 150 man-days = 300 boy-days ⇒ 1 man = 2 boys ⇒ 1 boy = 0.5 man. Step-by-Step Solution:10 men + 10 boys = 10 men + 5 men (equivalent) = 15 men.Job size in man-days = 150.Time = 150 man-days / 15 men = 10 days. Verification / Alternative check:Using rates: one man = 1/150 per day (for 15 men finishing in 10 days) ⇒ 10 men + 10 boys = 15 man-equivalent ⇒ 15/150 = 1/10 per day ⇒ 10 days. Why Other Options Are Wrong:8, 9, 11, 12 days arise from mixing the equivalence or job size computations. Common Pitfalls:Assuming additive days instead of additive rates; forgetting to convert 10 boys to 5 man-equivalent. Final Answer:10 days

Question 3

Isolating one worker’s time from group times: Ganesh, Ram, and Sohan together can do a work in 16 days. Ganesh and Ram together can do the same work in 24 days. How long will Sohan alone take to complete the work?

Accepted Answer

Introduction / Context:Subtract the pair rate from the triple rate to isolate Sohan’s rate, then invert to get his time alone. Given Data / Assumptions: G + R + S = 1/16 per day. G + R = 1/24 per day. Concept / Approach:Sohan’s rate = (G + R + S) − (G + R) = 1/16 − 1/24. Step-by-Step Solution:1/16 − 1/24 = (3 − 2)/48 = 1/48.Sohan alone time = 1 / (1/48) = 48 days. Verification / Alternative check:Check: 1/24 + 1/48 = 1/16 ⇒ consistent. Why Other Options Are Wrong:24, 36, 42, 40 days contradict the computed rate difference. Common Pitfalls:Adding 16 and 24 or taking an average instead of subtracting rates. Final Answer:48 days

Question 4

A leaves mid-way – remaining work by A alone: A and B can complete a work in 8 days working together. B alone can do it in 12 days. After working together for 4 days, B leaves. How many days will A take to complete the remaining work?

Accepted Answer

Introduction / Context:Use the given joint time and B’s solo time to isolate A’s solo rate. Then, after the initial joint period, compute the remaining work and the time A needs to finish it alone. Given Data / Assumptions: A + B = 1/8 work/day. B = 1/12 work/day ⇒ A = 1/8 − 1/12 = 1/24 work/day. First 4 days: both together. Concept / Approach:Compute work done in the first 4 days and then divide the remainder by A’s rate. Step-by-Step Solution:Work in first 4 days = 4 * (1/8) = 1/2.Remaining work = 1 − 1/2 = 1/2.A alone rate = 1/24 ⇒ time = (1/2) / (1/24) = 12 days. Verification / Alternative check:Check quickly: A would do the whole work in 24 days; finishing half takes 12 days. Why Other Options Are Wrong:10, 11, 13, 14 days mismatch the exact remaining half and A’s 1/24 per-day rate. Common Pitfalls:Using B’s 12-day time incorrectly or assuming 8 − 4 = 4 days naïvely. Final Answer:12 days

Question 5

After a joint start, one finishes the remainder: Ajay can do a work in 25 days and Sanjay in 20 days. They work together for 5 days, after which Ajay leaves. In how many days will Sanjay finish the remaining work alone?

Accepted Answer

Introduction / Context:Joint work first reduces the remaining fraction, then a single worker completes the rest at his own rate. Track fractions carefully. Given Data / Assumptions: Ajay = 1/25 per day; Sanjay = 1/20 per day. First 5 days: both work together. Concept / Approach:Compute work done in the first 5 days, subtract from 1, then divide the remainder by Sanjay’s rate. Step-by-Step Solution:Combined rate = 1/25 + 1/20 = 9/100 per day.Work in 5 days = 5 * 9/100 = 45/100 = 9/20.Remaining = 1 − 9/20 = 11/20.Sanjay’s rate = 1/20 ⇒ time = (11/20) / (1/20) = 11 days. Verification / Alternative check:Translate to 100-unit job: first 5 days produce 45 units; 55 remain; Sanjay at 5 units/day ⇒ 11 days. Why Other Options Are Wrong:9, 10, 12, 14 days misrepresent either the first 5-day output or Sanjay’s finishing rate. Common Pitfalls:Using averages of times instead of rates; arithmetic slips with fractions. Final Answer:11 days

Question 6

Back-infer B’s solo time from a shortfall scenario: A and B together can complete a work in 3 days. They start together, but after 2 days B leaves. The work finishes 2 days later (i.e., after 4 days total). How many days would B alone take to comple…

Accepted Answer

Introduction / Context:We know the pair’s rate and the actual timeline with B leaving. Express total work as the sum of two segments and solve for A’s rate first, then B’s time. Given Data / Assumptions: A + B = 1/3 per day. First 2 days: both work; last 2 days: A alone; total = full job. Concept / Approach:Compute: 2*(A + B) + 2*A = 1 ⇒ isolate A, then get B = 1/3 − A. Step-by-Step Solution:2*(1/3) + 2a = 1 ⇒ 2/3 + 2a = 1 ⇒ 2a = 1/3 ⇒ a = 1/6.Then b = 1/3 − 1/6 = 1/6.B alone time = 1 / (1/6) = 6 days. Verification / Alternative check:Check total: 2*(1/3) + 2*(1/6) = 2/3 + 1/3 = 1 ✔. Why Other Options Are Wrong:5, 7, 8, and 10 days do not match the deduced rate for B. Common Pitfalls:Assuming both have the same time from the start without solving; or misreading “2 more days”. Final Answer:6 days

Question 7

After initial teamwork, B completes the remainder: A and B together complete a job in 24 days. A alone can complete it in 32 days. Both work together for 8 days and then A leaves. How many days will B take to finish the remaining work?

Accepted Answer

Introduction / Context:Use A’s solo time and the joint time to infer B’s rate, then apply it to the remaining fraction after the initial collaboration. Given Data / Assumptions: A + B = 1/24 per day. A = 1/32 per day ⇒ B = 1/24 − 1/32 = 1/96 per day. First 8 days: both together. Concept / Approach:Compute initial completed portion, then divide the remainder by B’s rate. Step-by-Step Solution:Work in first 8 days = 8 * (1/24) = 1/3.Remaining work = 1 − 1/3 = 2/3.B alone time = (2/3) / (1/96) = 64 days. Verification / Alternative check:Rough check: B is slow (96 days alone), so 2/3 of the job indeed needs about 64 days. Why Other Options Are Wrong:16, 32, 48, and 40 days misapply either the initial 8-day contribution or B’s rate. Common Pitfalls:Subtracting times rather than rates; ignoring that only 1/3 was done initially. Final Answer:64 days

Question 8

Equivalent work (man-hour balancing): 20 workers working 5 hours per day finish a job in 10 days. If instead 25 workers are employed for 10 hours per day, how many days will be required to complete the same job?

Accepted Answer

Introduction / Context:With uniform productivity, total work is proportional to (workers × hours/day × days). Balance man-hours between the two scenarios to find the unknown days. Given Data / Assumptions: Scenario 1: 20 workers × 5 h/day × 10 days. Scenario 2: 25 workers × 10 h/day × D days. Concept / Approach:Set total man-hours equal between the two scenarios. Step-by-Step Solution:Total (1) = 20 * 5 * 10 = 1000 man-hours.Let D be required days in scenario (2): 25 * 10 * D = 1000 ⇒ 250D = 1000 ⇒ D = 4. Verification / Alternative check:Intuitively, scenario (2) has 2.5 times the daily man-hours (25 * 10 vs 20 * 5 = 250 vs 100), hence time shrinks by 1000/250 = 4 days. Why Other Options Are Wrong:3, 5, 6, 8 days do not preserve equality of total man-hours for the same job. Common Pitfalls:Comparing only workers or only hours per day without multiplying both. Final Answer:4 days

Question 9

Meeting a deadline by releasing workers: 90 men are engaged to finish a job in 40 days. After 25 days, 2/3 of the work is complete. How many men can be released so that the remaining work is finished on schedule (i.e., within the original 40 days)?

Accepted Answer

Introduction / Context:Use the observed progress to infer per-man productivity, then compute how many are needed to finish the remainder in the remaining days. The rest can be released. Given Data / Assumptions: Planned: 40 days total with 90 men. After 25 days, work done = 2/3. Remaining time = 40 − 25 = 15 days; remaining work = 1/3. Concept / Approach:Estimate daily team rate from progress so far, convert to per-man rate, and then deduce the required team size for the remainder. Step-by-Step Solution:Observed team rate = (2/3) / 25 = 2/75 per day.Per-man rate r = (2/75) / 90 = 1/3375 per day.Let N men work the last 15 days: N * r * 15 = 1/3 ⇒ N * (15/3375) = 1/3 ⇒ N/225 = 1/3 ⇒ N = 75.Men to release = 90 − 75 = 15. Verification / Alternative check:Check: 75 men for 15 days at 1/3375 each ⇒ 75 * 15 / 3375 = 1/3 ✔. Why Other Options Are Wrong:10, 20, 25, 30 would not hit exactly the remaining 1/3 in 15 days given the inferred per-man rate. Common Pitfalls:Assuming original planned rate instead of using actual measured progress; arithmetic slips with thirds. Final Answer:15

Question 10

Staggered team with A quitting early: A, B, and C can complete a work individually in 8, 12, and 15 days, respectively. A and B start together; after working for 2 days, A quits. Then C joins B and they continue till completion. In how many days (to…

Accepted Answer

Introduction / Context:Split the timeline: first 2 days with A + B, then B + C for the remainder. Convert all times to per-day rates, compute fractions done, and sum durations. Given Data / Assumptions: A = 1/8 per day. B = 1/12 per day. C = 1/15 per day. Days 1–2: A + B; thereafter: B + C. Concept / Approach:Work done first 2 days = 2 * (A + B). Remaining = 1 − that. Time to finish remainder = remaining / (B + C). Step-by-Step Solution:A + B = 1/8 + 1/12 = (3 + 2)/24 = 5/24.Work in 2 days = 2 * 5/24 = 10/24 = 5/12.Remaining = 1 − 5/12 = 7/12.B + C = 1/12 + 1/15 = (5 + 4)/60 = 9/60 = 3/20.Time for remainder = (7/12) / (3/20) = (7/12) * (20/3) = 35/9 days.Total time = 2 + 35/9 = 53/9 days. Verification / Alternative check:Approximation: 53/9 ≈ 5.888…, plausible since after an initial push, two moderate workers finish. Why Other Options Are Wrong:The other fractions do not equal 2 + (7/12)/(3/20) and thus misrepresent the segmented rates. Common Pitfalls:Adding times instead of rates; forgetting that A leaves after exactly 2 days. Final Answer:53/9 days

Question 11

A and B can complete a piece of work in 9 days and 18 days, respectively. However, due to illness, A is working at only 90% of usual efficiency and B at 72% of usual efficiency. If they work together at these reduced efficiencies, in how many days w…

Accepted Answer

Introduction / Context:Time-and-work problems often adjust worker efficiencies due to constraints like illness or fatigue. Here, A and B do not work at full capacity, so we must scale their normal rates and then combine the reduced rates to find the total time. Given Data / Assumptions: A's usual time = 9 days, B's usual time = 18 days. Reduced efficiency: A at 90%, B at 72%. They work together at these reduced efficiencies until completion. Concept / Approach:Convert times to rates, scale by efficiency, add rates to get the combined rate, then invert to get total time. Use rate = 1 / time. Multiply rates by the efficiency fraction when efficiency is reduced. Step-by-Step Solution: A's usual rate = 1/9 per dayA's reduced rate = 0.90 * (1/9) = 1/10B's usual rate = 1/18 per dayB's reduced rate = 0.72 * (1/18) = 0.04 = 1/25Combined reduced rate = 1/10 + 1/25 = (5 + 2)/50 = 7/50 per dayTotal time = 1 / (7/50) = 50/7 days = 7 1/7 days Verification / Alternative check:Approximate: If both worked at full efficiency, time would be 1 / (1/9 + 1/18) = 6 days. Reduced efficiencies should increase time above 6; 7.14 days is reasonable. Why Other Options Are Wrong: 8 days: Implies too low a combined rate compared to computed 7/50. 6 2/3 days: Still too optimistic for the given reductions. 7 1/2 days and 10 1/7 days: Do not match exact combined-rate inversion. Common Pitfalls:Using reduced time instead of reduced rate; forgetting to scale each person's rate by the efficiency percentage; adding times directly instead of rates. Final Answer:7 1/7 days

Question 12

A job is planned for 36 men to finish in 48 days. After 24 days, only 2/5 of the work is completed. How many additional men must be employed so that the work is still finished within the original 48-day schedule?

Accepted Answer

Introduction / Context:When progress lags behind schedule, we can increase the workforce to meet the deadline. We compare required man-days with what remains to determine the additional men needed. Given Data / Assumptions: Planned crew = 36 men for 48 days. After 24 days, only 2/5 of the work is done. Goal: finish by day 48 (24 more days). Concept / Approach:Total work can be expressed in man-days. Using progress data, infer the project’s true size, then compute remaining man-days and divide by remaining days to get the required headcount. Step-by-Step Solution: Planned production in 24 days = 36 * 24 = 864 man-daysBut this equals 2/5 of actual work → Total work = 864 * (5/2) = 2160 man-daysWork done = 864, Remaining = 2160 - 864 = 1296 man-daysDays left = 48 - 24 = 24 daysRequired men = 1296 / 24 = 54 menAdditional men = 54 - 36 = 18 Verification / Alternative check:54 men * 24 days = 1296 man-days remaining; matches need exactly. Why Other Options Are Wrong: 16, 14: Under-hire; would miss deadline. 20, 22: Over-hire; more than necessary given exact calculation. Common Pitfalls:Using planned total (36*48) as actual work without adjusting for the slower-than-expected progress; forgetting to subtract completed man-days before computing requirements. Final Answer:18

Question 13

Sixteen men working 18 hours per day can build a wall 36 m long, 4 m wide, and 24 m high in 20 days. How many men are required to build a wall 64 m long, 6 m wide, and 18 m high in 16 days if they work 12 hours per day?

Accepted Answer

Introduction / Context:This is a direct proportion problem where required effort is proportional to volume * men * hours * days. Changing any dimension or schedule scales the manpower requirement accordingly. Given Data / Assumptions: Case 1: 16 men, 18 h/day, 20 days → wall 36 × 4 × 24. Case 2: Unknown men M, 12 h/day, 16 days → wall 64 × 6 × 18. Concept / Approach:Use proportionality: (men * hours * days) ∝ volume. Set up a ratio between cases and solve for M. Step-by-Step Solution: Volume1 = 36*4*24 = 3456Volume2 = 64*6*18 = 6912(16*18*20)/3456 = (M*12*16)/6912M = 16 * (18*20*6912)/(12*16*3456) = 16 * (360*2)/192 = 16 * 720/192 = 60 Verification / Alternative check:Volume doubles (6912 vs 3456), but hours/day and days are reduced; the computed M reflects these counterbalancing effects and yields an integer 60. Why Other Options Are Wrong:They do not satisfy the proportionality when all factors (hours and days) are correctly accounted for. Common Pitfalls:Ignoring one of the scaling factors (hours or days) or mixing up volume dimensions. Final Answer:60

Question 14

A can finish a work alone in 5 days. With the help of his friend, the same work finishes in 3 days. In how many days can the friend alone complete the work?

Accepted Answer

Introduction / Context:When two people together complete faster than one person alone, the partner’s rate equals the joint rate minus the known individual rate. Invert the partner’s rate to get the partner’s time alone. Given Data / Assumptions: A alone = 5 days → rate 1/5. Together = 3 days → rate 1/3. Concept / Approach:Friend’s rate = (1/3) - (1/5). Time = 1 / (friend’s rate). Step-by-Step Solution: Friend's rate = 1/3 - 1/5 = (5 - 3)/15 = 2/15Friend's time = 1 / (2/15) = 15/2 = 7 1/2 days Verification / Alternative check:Combined check: 1/5 + 2/15 = 3/15 + 2/15 = 5/15 = 1/3 → matches together time 3 days. Why Other Options Are Wrong:They do not satisfy the rate difference or inverse relationship implied by the given data. Common Pitfalls:Subtracting times instead of rates; forgetting to invert the final rate to get time. Final Answer:7 1/2 days

Question 15

A and B can complete a work alone in 15 days and 25 days, respectively. They start together, but B leaves after some time and A finishes the remaining work in the last 7 days. After how many days from the start did B leave?

Accepted Answer

Introduction / Context:When one worker leaves before completion, split the work into two phases: joint phase and solo phase. Use rates to form an equation for the total work. Given Data / Assumptions: A = 1/15 per day; B = 1/25 per day. A alone finishes the last 7 days. Let x = days they worked together. Concept / Approach:Work done = x*(A+B) + 7*A = 1. Solve for x. Step-by-Step Solution: A+B = 1/15 + 1/25 = 8/75Equation: x*(8/75) + 7*(1/15) = 17/15 = 35/75; 1 - 35/75 = 40/75 = 8/15x = (8/15) / (8/75) = 75/15 = 5 Verification / Alternative check:Check totals: 5*(8/75) = 8/15; plus 7/15 = 1 → consistent. Why Other Options Are Wrong:They do not satisfy the total-work equation when rates are used correctly. Common Pitfalls:Equating times instead of work; arithmetic slips when converting to common denominators. Final Answer:5

Question 16

A can complete a work in 20 days and B in 30 days. A works alone for 4 days, after which B and C together complete the remaining work in 18 days. In how many days can C alone complete the entire work?

Accepted Answer

Introduction / Context:We first deduct the portion done by A, then use the joint duration of B and C to solve for C's rate. Finally, invert to get C's solo time. Given Data / Assumptions: A = 1/20 per day; B = 1/30 per day. A works 4 days → work done = 4/20 = 1/5. Remaining work = 4/5 completed by (B + C) in 18 days. Concept / Approach:(B + C) rate = remaining work / time. Subtract B's rate to get C's rate; then invert for time. Step-by-Step Solution: (B + C) rate = (4/5) / 18 = 4/90 = 2/45C's rate = (2/45) - (1/30) = (4 - 3)/90 = 1/90C alone time = 1 / (1/90) = 90 days Verification / Alternative check:Back-substitute: In 18 days, B does 18*(1/30)=3/5; C does 18*(1/90)=1/5; total 4/5 → consistent. Why Other Options Are Wrong:Do not match the derived C rate; misinterpretation of the staged work often leads to wrong values like 72 or 84. Common Pitfalls:Forgetting to subtract A's initial contribution; mixing up rates and times when combining workers. Final Answer:90

Question 17

Six men can finish a work in 12 days; eight women can finish it in 18 days; and eighteen children can finish it in 10 days. First, 4 men, 12 women, and 20 children work together for 2 days. If only men must finish the remaining work in 1 additional …

Accepted Answer

Introduction / Context:Convert each group's capability into an equivalent daily rate per individual, then add contributions over the first phase. The remainder is completed by men in a final 1-day push. Given Data / Assumptions: 6 men → 12 days → 72 man-days → 1 man = 1/72 per day. 8 women → 18 days → 144 woman-days → 1 woman = 1/144 per day. 18 children → 10 days → 180 child-days → 1 child = 1/180 per day. Concept / Approach:Compute the fraction of work done in first 2 days, then set n*(1/72) = remaining work (to be done in 1 day) to find n. Step-by-Step Solution: Daily combined rate = 4*(1/72) + 12*(1/144) + 20*(1/180)= 1/18 + 1/12 + 1/9 = 1/4 per dayWork in 2 days = 1/2; Remaining = 1/2Let required men = n; In 1 day: n*(1/72) = 1/2 → n = 36 Verification / Alternative check:Cross-check equivalences: woman = 1/144 = half of man; child ≈ 0.4 of man; totals align to 1/4 per day. Why Other Options Are Wrong:Undershoot or overshoot the exact half-work remaining within a single day. Common Pitfalls:Arithmetic slips when summing heterogeneous rates; forgetting that the final phase is only 1 day. Final Answer:36

Question 18

A, B, and C can do a job in 18, 24, and 36 days, respectively. They work on alternate days in the order: Day 1 – C, Day 2 – B, Day 3 – A, Day 4 – C, and so on. In how many days will the work be finished?

Accepted Answer

Introduction / Context:With alternating workers, compute the work done per full cycle and then scale up to cover the entire job. A 3-day cycle repeats until completion. Given Data / Assumptions: A = 1/18, B = 1/24, C = 1/36 per day. Order: C, B, A, then repeats. Concept / Approach:Per 3-day cycle work = sum of daily rates in order. Divide 1 by the cycle sum to get number of cycles; multiply by 3 for days. Step-by-Step Solution: Cycle work = 1/36 + 1/24 + 1/18= (2 + 3 + 4)/72 = 9/72 = 1/8Total cycles = 1 / (1/8) = 8 cyclesTotal days = 8 * 3 = 24 Verification / Alternative check:Each cycle contributes exactly 1/8 of the job; 8 cycles complete it. Why Other Options Are Wrong:They do not match the exact cycle-sum fraction. Common Pitfalls:Adding times instead of rates or mis-ordering the pattern. Final Answer:24

Question 19

Sixteen children and twenty-four men can finish a job in 18 days. If each child takes twice as long as each man to do the job alone (i.e., a child is half as efficient as a man), in how many days will 24 men finish the same job?

Accepted Answer

Introduction / Context:The statement that a child takes twice the time a man takes implies each child's daily rate is half that of a man. Use equivalent-man units to compute the team's rate and then the time for 24 men alone. Given Data / Assumptions: 16 children + 24 men finish in 18 days. Child = 1/2 man in efficiency. Concept / Approach:Convert children to man-equivalents, compute total daily man-equivalents, find job size in man-days, then divide by 24 men. Step-by-Step Solution: Equivalent men per day = 24 + 16*(1/2) = 24 + 8 = 32Job size = 32 * 18 = 576 man-daysTime for 24 men = 576 / 24 = 24 days Verification / Alternative check:Proportional scaling with equivalent units yields an integer result, indicating internal consistency. Why Other Options Are Wrong:They represent incorrect conversions or divisions when moving between mixed crews and a men-only crew. Common Pitfalls:Misreading the phrase “twice the time” as “twice as efficient”; always convert carefully. Final Answer:24 days

Question 20

A takes twice as long as B to finish a job, and C takes three times as long as B. Working together, they finish the job in 12 days. How many days would A take to do the job alone?

Accepted Answer

Introduction / Context:Express all times relative to B. Convert to rates, add to get the joint rate, equate to the given joint time, and back out A’s time. Given Data / Assumptions: A = 2B, C = 3B (in time). Together time = 12 days. Concept / Approach:If B needs t days, then rates are: A = 1/(2t), B = 1/t, C = 1/(3t). Sum to get 11/(6t). Set 12 * 11/(6t) = 1 to solve for t and then 2t. Step-by-Step Solution: Joint rate = 1/(2t) + 1/t + 1/(3t) = 11/(6t)12 * (11/(6t)) = 1 → 22/t = 1 → t = 22A alone time = 2t = 44 days Verification / Alternative check:Compute joint rate with t=22: 1/44 + 1/22 + 1/66 = 1/12 → consistent. Why Other Options Are Wrong:They correspond to incorrect algebra when resolving t or doubling to get A’s time. Common Pitfalls:Adding times rather than rates; mixing up “takes twice the time” with “twice as efficient.” Final Answer:44

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