Question 1

6 men + 8 boys finish a job in 10 days; 26 men + 48 boys finish the same job in 2 days. In how many days will 15 men + 20 boys finish it?

Accepted Answer

Problem restatementGiven two group-productivity scenarios, deduce the individual efficiency of a man and a boy, then compute the time for a third team. Given data (6m + 8b) × 10 = 1 job → 6m + 8b = 1/10. (26m + 48b) × 2 = 1 job → 26m + 48b = 1/2. Concept/ApproachLet m, b be daily job-fractions of one man and one boy. Solve the linear system for m and b; then compute (15m + 20b) and invert to get time. Step-by-step calculation 6m + 8b = 1/10 … (1) 26m + 48b = 1/2 … (2) From (1): m = (1/10 − 8b)/6 Substitute in (2): 26(1/10 − 8b)/6 + 48b = 1/2 (13/3)(1/10 − 8b) + 48b = 1/2 13/30 − (104/3)b + 48b = 1/2 13/30 + (40/3)b = 1/2 → (40/3)b = 1/2 − 13/30 = 1/15 b = (1/15) × (3/40) = 1/200 Then from (1): 6m = 1/10 − 8(1/200) = 1/10 − 1/25 = 3/50 → m = 1/100 For 15 men + 20 boys: rate = 15m + 20b = 15/100 + 20/200 = 0.15 + 0.10 = 0.25 = 1/4 job/day Time = 1 ÷ (1/4) = 4 days VerificationPlug m = 1/100, b = 1/200 back into (2): 26/100 + 48/200 = 0.26 + 0.24 = 0.50 = 1/2 (correct). Common pitfalls Forgetting to convert group-time statements into per-day equations first. Arithmetic errors when handling fractions; keep exact fractions to avoid rounding mistakes. Final Answer4 days

Question 2

Sakshi can finish a job in 20 days. Tanya is 25% more efficient than Sakshi. In how many days can Tanya finish the same job?

Accepted Answer

Problem restatementGiven Tanya is 25% more efficient (faster) than Sakshi, compute Tanya's time from Sakshi's time. Given data Sakshi's time = 20 days → rate S = 1/20 job/day. Tanya's efficiency = 1.25 × S → rate T = 1.25 × (1/20) = 1/16 job/day. Concept/ApproachTime is inverse of rate. If efficiency increases by 25%, time multiplies by 1/1.25. Step-by-step calculation Tanya's time = 20 ÷ 1.25 = 16 days VerificationDirect inverse check: rate 1/16 indeed corresponds to 16 days. Common pitfalls Adding 25% to time (incorrect). The 25% applies to rate, not time. Final Answer16 days

Question 3

A finishes a work in 18 days, B in 15 days. B works for 10 days and leaves. In how many days will A alone finish the remaining work?

Accepted Answer

Problem restatementWith different solo times for A and B, B contributes for 10 days first. Compute the leftover work for A and the time needed. Given data A's time = 18 days → A's rate = 1/18 job/day. B's time = 15 days → B's rate = 1/15 job/day. B works 10 days. Concept/ApproachWork done = rate × time. Remaining = 1 − (B's contribution). Step-by-step calculation Work by B in 10 days = 10 × (1/15) = 2/3 Remaining work = 1 − 2/3 = 1/3 Time for A = (1/3) ÷ (1/18) = 6 days VerificationEquivalent unit method: LCM 90 units. B does 6 units/day × 10 = 60; remaining 30 units; A does 5/day → 6 days. Common pitfalls Subtracting days instead of subtracting work. Final Answer6 days

Question 4

A and B together finish a job in 30 days. A works alone for 16 days; B then finishes the remainder alone in 44 days. In how many days can B alone finish the whole job?

Accepted Answer

Problem restatementWe know the joint time for (A + B), a head start by A, and the finishing time by B alone. Find B's solo time. Given data a + b = 1/30 (job/day). A works 16 days alone: work = 16a. B finishes the rest in 44 days: 44b = 1 − 16a. Concept/ApproachExpress a = 1/30 − b and substitute into the remainder equation to solve for b. Step-by-step calculation 44b = 1 − 16(1/30 − b) = 1 − 16/30 + 16b = 1 − 8/15 + 16b = 7/15 + 16b 44b − 16b = 7/15 → 28b = 7/15 → b = 1/60 Therefore, B's time = 1 ÷ b = 60 days VerificationThen a = 1/30 − 1/60 = 1/60; A's 16 days produce 16/60 = 4/15 of the job; remainder 11/15 finished by B in 44 days → 44 × (1/60) = 11/15 (consistent). Common pitfalls Using 30 − 16 − 44 style arithmetic on days (invalid); must use rates and work. Final Answer60 days

Question 5

A, B, C can complete a work in 24, 6, and 12 days respectively. Working together, how long will they take to complete the work?

Accepted Answer

Problem restatementCombine individual rates of A, B, and C to get a joint completion time. Given data A's time = 24 days → rate = 1/24. B's time = 6 days → rate = 1/6. C's time = 12 days → rate = 1/12. Concept/ApproachIndependent workers' rates add: joint rate = 1/24 + 1/6 + 1/12. Step-by-step calculation Joint rate = 1/24 + 1/6 + 1/12 = 1/24 + 4/24 + 2/24 = 7/24 job/day Joint time = 1 ÷ (7/24) = 24/7 days 24/7 days ≈ 3.4286 days ≈ 3 days 10 hours 17 minutes VerificationIn 24/7 days, total work = (7/24) × (24/7) = 1 (exact). Common pitfalls Taking average of times (24, 6, 12) rather than adding rates. Final Answer24/7 days (≈ 3 days 10 hours)

Question 6

A can finish a job in 24 days, B in 9 days, and C in 12 days. B and C work together for 3 days; A completes the remainder. How many days does A take for the remainder?

Accepted Answer

Problem restatementTwo faster workers (B, C) start and then leave; compute remaining work for A and the time A needs. Given data A's rate = 1/24 job/day. B's rate = 1/9 job/day. C's rate = 1/12 job/day. B and C work together for 3 days. Concept/ApproachFirst compute the fraction completed by (B + C) in 3 days, subtract from 1 to get the remainder, then divide by A's rate. Step-by-step calculation (B + C) rate = 1/9 + 1/12 = 7/36 Work done in 3 days = 3 × (7/36) = 7/12 Remainder = 1 − 7/12 = 5/12 Time for A = (5/12) ÷ (1/24) = (5/12) × 24 = 10 days VerificationUnit-check: 10 days at 1/24 per day completes 10/24 = 5/12, equal to the remainder. Common pitfalls Multiplying instead of dividing by A's rate when converting remainder to time. Final Answer10 days

Question 7

A alone can do a job in 4 hours; (B + C) together in 3 hours; (A + C) together in 2 hours. How long will B alone take?

Accepted Answer

Problem restatementGiven three composite times involving A, B, and C, find B's solo time. Given data a = 1/4 job/hour. b + c = 1/3 job/hour. a + c = 1/2 job/hour. Concept/ApproachIsolate c from (a + c), then subtract from (b + c) to get b. Step-by-step calculation c = (a + c) − a = 1/2 − 1/4 = 1/4 b = (b + c) − c = 1/3 − 1/4 = (4 − 3)/12 = 1/12 job/hour B's time = 1 ÷ (1/12) = 12 hours VerificationCheck consistency: a = 1/4, c = 1/4 → (a + c) = 1/2 (given). Then (b + c) = 1/12 + 1/4 = 1/3 (given). Common pitfalls Adding or subtracting the times rather than the rates. Final Answer12 hours

Question 8

A completes 80% of a work in 20 days. A and B together finish the remaining work in 3 days. How long would B alone take to do the whole work?

Accepted Answer

Problem restatementFrom A's partial-completion time and the joint finishing time with B, find B's solo time for the entire job. Given data A completes 80% (0.8) in 20 days → A's rate = 0.8/20 = 0.04 = 1/25 job/day. Remaining work = 20% = 0.2. (A + B) finish 0.2 in 3 days → (A + B) rate = 0.2/3 = 1/15 job/day. Concept/ApproachCompute B's rate by subtracting A's rate from the combined rate, then invert to get B's time for 1 job. Step-by-step calculation A's rate = 1/25 (A + B) rate = 1/15 B's rate = 1/15 − 1/25 = (5 − 3)/75 = 2/75 job/day B's time = 1 ÷ (2/75) = 75/2 = 37.5 days Verification/AlternativeCheck the finish segment: In 3 days, A contributes 3 × 1/25 = 0.12; B contributes 3 × (2/75) = 0.08; total = 0.20 (the remaining 20%). Common pitfalls Assuming A's 20-day time is for the full job; it is for 80% only. Subtracting times instead of subtracting rates to get B's speed. Final Answer37.5 days

Question 9

A is 30% more efficient than B. If A alone can complete a job in 23 days, how long will A and B together take to finish it?

Accepted Answer

Problem restatementA is 30% more efficient than B. A alone takes 23 days. Find the joint time of A and B working together. Given data A's time alone = 23 days ⇒ A's rate = 1÷23 job/day. A is 30% more efficient than B ⇒ rA = 1.3 × rB. Concept/ApproachConvert the efficiency statement into rates. From rA = 1.3 rB, obtain rB. Then add rates to get the combined time. Step-by-step calculationrA = 1÷23r = r÷1.3 = (1÷23)÷1.3 = 1÷(23 × 1.3)Combined rate = r + r = 1÷23 + 1÷(23 × 1.3) = (1 + 1÷1.3) ÷ 231 + 1÷1.3 = 1 + 10÷13 = 23÷13So combined rate = (23÷13) ÷ 23 = 1÷13 job/dayTime together = 1 ÷ (1÷13) = 13 days Verification/AlternativeLet B's rate be b. Then A's rate = 1.3b. If A = 1÷23, then 1.3b = 1÷23 ⇒ b = 1÷29.9. Sum = 1÷23 + 1÷29.9 ≈ 0.076923… ⇒ time ≈ 13 days. Common pitfallsInterpreting “30% more efficient” as time reduction instead of rate increase. The percentage applies to rate, not days. Final Answer13 days

Question 10

A and B can complete a work together in 30 days. They work together for 20 days; then B leaves, and A finishes the remaining work in the next 20 days. In how many days can A alone finish the work?

Accepted Answer

Problem restatementThe pair completes a project in 30 days. After 20 days of working together, B leaves; A alone completes the rest in 20 days. Find A's solo time. Given data (A + B) time = 30 days ⇒ (A + B) rate = 1÷30 per day. First phase: 20 days together. Second phase: 20 days by A alone. Concept/ApproachCompute the fraction completed in phase 1; the remainder is done by A in phase 2, which gives A's rate. Step-by-step calculationWork done in first 20 days = 20 × (1÷30) = 2÷3Remaining work = 1 − 2÷3 = 1÷3A completes 1÷3 in 20 days ⇒ A's rate = (1÷3) ÷ 20 = 1÷60 per dayTherefore, A's time alone = 60 days Verification/AlternativeCheck units: rate in job/day times days gives fraction of job, consistent in both phases. Common pitfallsForgetting that only A works in the last 20 days; mixing average of 30 and 20 without using rates is incorrect. Final Answer60 days

Question 11

By walking at only three-fourths (3/4) of his usual speed, a person reaches his office 20 minutes later than he normally does. What is his usual (normal) time to cover the same route?

Accepted Answer

Introduction / Context: This problem tests proportional reasoning between speed and time. When speed changes by a factor, the travel time changes inversely by the same factor. Understanding this inverse relation allows us to translate a given delay into the original time. Given Data / Assumptions: Reduced speed = 3/4 of usual speed. Extra time (delay) due to reduced speed = 20 minutes. Route distance is the same in both cases. Concept / Approach: Time is inversely proportional to speed for a fixed distance. If speed scales by k, then time scales by 1/k. Here, reduced speed factor is 3/4, so the new time factor is 4/3 of the usual time. The difference between new and usual time equals the given delay. Step-by-Step Solution: Let T = usual time (minutes). Reduced speed time = (4/3) * T. Delay = ((4/3) * T) - T = (1/3) * T. Given delay = 20 ⇒ (1/3) * T = 20 ⇒ T = 60 minutes. Verification / Alternative check: If usual time is 60 minutes, reduced-speed time is 60 * 4/3 = 80 minutes, which is indeed 20 minutes more. Checks out. Why Other Options Are Wrong: 30 min: Would give delay 10 min, not 20. 75 min: Would give delay 25 min. 1 hr 30 min: Implies a much larger delay. 45 min: Would give delay 15 min. None match the 20-minute delay. Common Pitfalls: Mixing up direct versus inverse proportionality and adding 25% to time instead of multiplying by 4/3 are common mistakes. Final Answer: 60 minutes

Question 12

A man travels a total of 35 km partly at 4 km/h and partly at 5 km/h. If he instead travels the earlier portion at 5 km/h and the later portion at 4 km/h, he could cover 2 km more in the same total time. Find the original total time taken.

Accepted Answer

Introduction / Context: This is a time–speed–distance puzzle using two speed segments. Swapping speeds between segments while holding the same total time allows forming equations based on time spent in each segment. Given Data / Assumptions: Total distance originally = 35 km. Original speeds: first part at 4 km/h, second part at 5 km/h. When speeds are swapped, distance covered in the same total time increases by 2 km. Concept / Approach: Let t1 and t2 be times on the two parts. Then original distance = 4t1 + 5t2 = 35. If speeds are swapped for the same times, the distance becomes 5t1 + 4t2, which is 2 km more than before: 5t1 + 4t2 = 37. Solving these gives t1 and t2; the total time is T = t1 + t2. Step-by-Step Solution: Original: 4t1 + 5t2 = 35. Swapped: 5t1 + 4t2 = 37. Subtract: (5t1 + 4t2) − (4t1 + 5t2) = 37 − 35 ⇒ t1 − t2 = 2. Use 4t1 + 5t2 = 35 and t1 = t2 + 2: 4(t2 + 2) + 5t2 = 35 ⇒ 9t2 + 8 = 35 ⇒ 9t2 = 27 ⇒ t2 = 3 h. Then t1 = 5 h, so total time T = t1 + t2 = 8 h. Verification / Alternative check: Original distance = 4*5 + 5*3 = 20 + 15 = 35 km. Swapped distance = 5*5 + 4*3 = 25 + 12 = 37 km, which is exactly 2 km more in the same 8 hours. Why Other Options Are Wrong: 9 h, 7 h, 4.5 h, 6 h do not satisfy both equations simultaneously; only 8 h fits both conditions. Common Pitfalls: Assuming the same distances rather than the same times after swapping speeds, or attempting to average speeds arithmetically instead of using segment times. Final Answer: 8 hours

Question 13

Six men or ten women can reap a field in 15 days. How many days will it take for a team of 12 men and 5 women to reap the same field?

Accepted Answer

Introduction / Context: This is a classic work-rate comparison. We convert all workers to a common efficiency unit (e.g., woman equivalents) using given equivalences and then compute the time for a mixed team. Given Data / Assumptions: 6 men can finish in 15 days. 10 women can finish in 15 days. Goal: time for 12 men and 5 women working together. Concept / Approach: Total work W is the same. With 10 women finishing in 15 days, W = 10w * 15 (where w = one woman's daily work). With 6 men finishing in 15 days, W = 6m * 15 (m = one man's daily work). Equating gives a relation between m and w, then find the mixed team's rate and compute days = W / rate. Step-by-Step Solution: From 6 men in 15 days: W = 6m * 15 = 90m. From 10 women in 15 days: W = 10w * 15 = 150w. Equate 90m = 150w ⇒ m = (150/90)w = (5/3)w. Mixed team daily rate = 12m + 5w = 12*(5/3)w + 5w = 20w + 5w = 25w. Total work W = 150w. Days = W / rate = 150w / 25w = 6 days. Verification / Alternative check: Using man-units: m = (5/3)w ⇒ 12 men = 12*(5/3)w = 20w; add 5w = 25w as above. Correct consistency. Why Other Options Are Wrong: 5, 8, 9, 12 days do not match the computed ratio-based result from the given equivalence; only 6 days fits the combined rate calculation. Common Pitfalls: Averaging days directly instead of converting to rates, or forgetting to convert all workers to a common unit before adding rates. Final Answer: 6 days

Question 14

Six children and two men complete a job in 6 days. Each child takes twice as long as a man to finish the work alone (i.e., a child is half as efficient as a man). In how many days can five men alone finish the same work?

Accepted Answer

Introduction / Context: This problem converts different worker types into a single efficiency scale. Given a child takes twice the time of a man alone, a child’s rate is half of a man’s rate. We use the team’s combined rate to deduce total work and then compute the time for five men. Given Data / Assumptions: 6 children + 2 men finish in 6 days. Child is half as efficient as a man. Find days for 5 men alone. Concept / Approach: Let m = one man’s daily work; then one child = m/2 per day. Compute the team’s daily rate, multiply by days to get total work W. Then divide W by 5m to find the required days. Step-by-Step Solution: One child’s rate = m/2. Team daily rate = 6*(m/2) + 2*m = 3m + 2m = 5m. Total work W = (team rate) * days = 5m * 6 = 30m. Five men’s daily rate = 5m. Required days = W / (5m) = 30m / 5m = 6 days. Verification / Alternative check: If one man alone needed T days, five men would need T/5; the calculations above are consistent with standard work-rate relations. Why Other Options Are Wrong: 8, 9, 10, 15 days contradict the direct rate computation of total work and five-men rate. Common Pitfalls: Confusing “takes twice the time” with “twice the efficiency,” or adding times instead of adding rates. Final Answer: 6 days

Question 15

Two men or five women or seven boys can finish a work in 469 days. In how many days will seven men, five women, and two boys together finish the same work?

Accepted Answer

Introduction / Context: We are given interchangeable work groups. From the common completion time, we deduce each individual’s daily work rate and then sum mixed rates to get the combined completion time. Given Data / Assumptions: 2 men finish in 469 days. 5 women finish in 469 days. 7 boys finish in 469 days. Find days for 7 men + 5 women + 2 boys. Concept / Approach: If a group finishes in D days, daily group rate = 1/D of the work. Hence one man’s daily rate = (1/469)/2, etc. After finding each single rate, sum the mixed team’s daily rate and invert to get days. Step-by-Step Solution: Let total work = 1. 2 men rate = 1/469 ⇒ 1 man = 1/938 per day. 5 women rate = 1/469 ⇒ 1 woman = 1/2345 per day. 7 boys rate = 1/469 ⇒ 1 boy = 1/3283 per day. Mixed team rate = 7*(1/938) + 5*(1/2345) + 2*(1/3283). Compute exactly: this sum simplifies to 1/98 per day (can be checked by common-denominator arithmetic). Required days = 1 / (1/98) = 98 days. Verification / Alternative check: Using a calculator or fraction arithmetic confirms the sum equals 1/98. Hence the time is 98 days. Why Other Options Are Wrong: 134, 106, 100, 96 days do not match the combined rate computed from the equivalences provided. Common Pitfalls: Assuming proportionality between numbers of workers and days without establishing consistent single-worker rates; forgetting to invert summed rate to get time. Final Answer: 98 days

Question 16

A total of 314 weavers weave 6594 shawls in one-sixth (1/6) of an hour (i.e., 10 minutes). On average, how many shawls does one weaver weave per hour?

Accepted Answer

Introduction / Context: This is a straightforward unit-rate calculation: total items produced divided by total worker-hours yields a per-worker per-hour productivity figure. Given Data / Assumptions: Total shawls = 6594. Total weavers = 314. Total time = 1/6 hour. Concept / Approach: Average output per weaver per hour = (total shawls) / (total weaver-hours) = 6594 / (314 * 1/6). Step-by-Step Solution: Total weaver-hours = 314 * (1/6) = 314/6 hours. Average rate per weaver per hour = 6594 / (314/6) = 6594 * 6 / 314. Compute 6594 * 6 = 39564. Now 39564 / 314 = 126. Hence, each weaver averages 126 shawls per hour. Verification / Alternative check: Multiply back: 126 shawls/hour * 314 weavers * (1/6) hour = 126 * 314 / 6 = 126 * 52.333… = 6594. Matches the given total. Why Other Options Are Wrong: 42, 21, 84, 102 are lower than the computed exact average; they arise from dividing by the number of weavers or time incorrectly. Common Pitfalls: Forgetting to multiply by 6 when converting 10 minutes (1/6 hour) to hourly rate; dividing by workers before accounting for time properly. Final Answer: 126

Question 17

The efficiencies (work rates) of A, B, and C are in the ratio 6 : 5 : 4. If they receive a total of ₹ 27000 for completing the job and payment is distributed in proportion to individual work done, what is C’s share?

Accepted Answer

Introduction / Context: When people work together for the same duration, the share of wages proportional to work done equals the ratio of their efficiencies. This question directly applies proportional division. Given Data / Assumptions: Efficiency ratio A : B : C = 6 : 5 : 4. Total payment = ₹ 27000. They all work for the same time period. Concept / Approach: If time is common, work done by each ∝ efficiency. Hence, payment shares are in the same ratio 6 : 5 : 4. Sum the parts and allocate to C accordingly. Step-by-Step Solution: Total parts = 6 + 5 + 4 = 15. C’s share = (4/15) * 27000 = 4 * 1800 = ₹ 7200. Verification / Alternative check: A’s share = (6/15)*27000 = ₹ 10800; B’s share = (5/15)*27000 = ₹ 9000; C’s share = ₹ 7200. Sum = 10800 + 9000 + 7200 = ₹ 27000. Correct. Why Other Options Are Wrong: ₹ 2700, ₹ 6300, ₹ 6000, ₹ 14400 do not match the proportional split with ratio 6 : 5 : 4 on ₹ 27000. Common Pitfalls: Dividing equally instead of proportionally, or mixing up the ratio order for A, B, and C. Final Answer: ₹ 7200

Question 18

If two men or three women or four boys can complete a job in 52 days, then how many days will one man, one woman, and one boy together take to complete the same job?

Accepted Answer

Introduction / Context: This question uses equivalent worker groups to derive single-worker rates and then sums those rates for a mixed team. It is a standard application of work-rate addition. Given Data / Assumptions: 2 men can finish in 52 days ⇒ group rate = 1/52 per day. 3 women can finish in 52 days. 4 boys can finish in 52 days. Find time for 1 man + 1 woman + 1 boy. Concept / Approach: Convert each to single-worker daily rate by dividing the group rate by the number in the group. Then add one man’s, one woman’s, and one boy’s daily rates, and invert to get the number of days. Step-by-Step Solution: Let total work = 1. 2 men rate = 1/52 ⇒ 1 man = 1/104 per day. 3 women rate = 1/52 ⇒ 1 woman = 1/156 per day. 4 boys rate = 1/52 ⇒ 1 boy = 1/208 per day. Mixed daily rate = 1/104 + 1/156 + 1/208 = 1/48. Hence days = 1 / (1/48) = 48 days. Verification / Alternative check: Common denominator arithmetic confirms 1/104 + 1/156 + 1/208 equals 1/48 exactly. Why Other Options Are Wrong: 36, 40, 45 days or “none of these” do not match the exact rate sum inversion of 48 days. Common Pitfalls: Averaging the given days or people counts instead of converting to per-person rates; forgetting to invert the total rate for time. Final Answer: 48 days

Question 19

A contractor planned to finish a project in 60 days. After 20 days, only one-fifth (1/5) of the work was completed with 75 workers employed. To finish on time, how many additional workers are required for the remaining 40 days (assume output is prop…

Accepted Answer

Introduction / Context: This is a workforce planning question. If progress lags behind schedule, we can scale workforce proportionally to required daily completion rates to meet the deadline. Given Data / Assumptions: Total target duration = 60 days. After 20 days, completed = 1/5 of work (20%). Initial workforce = 75 workers. Output is proportional to the number of workers. Concept / Approach: Compute current daily completion rate and the required daily rate for the remaining period. The ratio of required to current rate gives the factor by which the workforce must be increased. Step-by-Step Solution: Current progress: 1/5 in 20 days ⇒ current rate = (1/5)/20 = 1/100 per day. Remaining work = 4/5; remaining time = 40 days. Required rate = (4/5)/40 = 1/50 per day. Factor needed = (required rate) / (current rate) = (1/50) / (1/100) = 2. Therefore, workforce must double from 75 to 150. Additional workers = 150 − 75 = 75. Verification / Alternative check: With 150 workers at twice the initial rate, 1/50 per day * 40 days = 4/5, perfectly matching the remaining work. Why Other Options Are Wrong: 25 or 50 insufficient; “can’t be determined” is incorrect because proportionality is given; 30 is arbitrary. Common Pitfalls: Comparing elapsed time to completed fraction without computing daily rates; forgetting to scale workforce based on required daily completion rate. Final Answer: 75

Question 20

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

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