Question 1

Work and Wages – Wage split by efficiency (rates add when working together): Shantanu completes a job in 12 days; Manu completes the same job in 10 days. If they work together and are paid proportionally to work done, in what ratio should their wage…

Accepted Answer

Introduction / Context:When workers are paid according to contribution, their wage shares are proportional to the amount of work each performs. For constant-rate workers, that equals their rates (work per day). Combining workers adds rates, but the internal split uses their individual rates. Given Data / Assumptions: Shantanu’s time = 12 days ⇒ rate = 1/12 job/day Manu’s time = 10 days ⇒ rate = 1/10 job/day Payment split is proportional to rates. Concept / Approach:Wage ratio = (1/12) : (1/10). Multiply through by the LCM to clear denominators and get clean integers for the ratio. Step-by-Step Solution:(1/12) : (1/10) = 10 : 12Simplify 10 : 12 to 5 : 6 Verification / Alternative check:Using a common-work model: in 60 days (LCM), Shantanu would do 5 units, Manu 6 units; hence wages 5:6. Why Other Options Are Wrong:3:2, 1:6, and 5:7 do not match the reciprocal-time ratio; 6:5 reverses the correct order. Common Pitfalls:Splitting by times taken (12:10) instead of by rates; remember wage ∝ rate, not time. Final Answer:5 : 6

Question 2

Work and Wages – Share by work rate when working together: A completes the work alone in 9 days; B alone in 15 days. If they work together and split wages proportional to contribution, what is the ratio A : B?

Accepted Answer

Introduction / Context:With constant rates, the share of wages for each worker equals the share of total work done, i.e., the worker’s rate compared to the team’s rate. This is a straightforward ratio of reciprocals of the individual times. Given Data / Assumptions: A’s time = 9 days ⇒ rate = 1/9 B’s time = 15 days ⇒ rate = 1/15 Concept / Approach:Wage ratio A:B = (1/9):(1/15) = 15:9, which simplifies to 5:3. This uses the principle that faster worker receives proportionally more. Step-by-Step Solution:(1/9):(1/15) = 15:9Simplify ⇒ 5:3 Verification / Alternative check:Use 45-unit model: A does 5 units/day, B does 3 units/day, so shares 5:3. Why Other Options Are Wrong:3:5 reverses the correct order; others do not reduce from 15:9. Common Pitfalls:Dividing by days directly; remember rates (reciprocals) determine shares. Final Answer:5 : 3

Question 3

Work and Wages – Split a fixed payment ₹ 900 by efficiency: A alone completes a job in 8 days; B alone in 10 days. They finish together and earn ₹ 900. Find each person’s share.

Accepted Answer

Introduction / Context:Total wages must be split according to each worker’s contribution, which for constant rates equals the worker’s rate. The combined completion does not change the internal ratio of contributions. Given Data / Assumptions: A’s time = 8 days ⇒ rate = 1/8 B’s time = 10 days ⇒ rate = 1/10 Total payment = ₹ 900 Concept / Approach:Wage ratio A:B = (1/8):(1/10) = 10:8 = 5:4. Split ₹ 900 in the ratio 5:4 to get individual shares. Step-by-Step Solution:Total parts = 5 + 4 = 9A’s share = 5/9 * 900 = ₹ 500B’s share = 4/9 * 900 = ₹ 400 Verification / Alternative check:Check sum: ₹ 500 + ₹ 400 = ₹ 900, as required. Why Other Options Are Wrong:Other splits do not match the 5:4 ratio generated by rates 1/8 and 1/10. Common Pitfalls:Allocating by days (8:10) instead of rates (1/8:1/10). Final Answer:A = ₹ 500 and B = ₹ 400

Question 4

Work and Wages – Share of A from total ₹ 225 when A and B work together: A alone finishes in 3 days; B alone in 2 days. They complete the work together; total wages = ₹ 225. Find A’s share.

Accepted Answer

Introduction / Context:Payment division for joint work is proportional to work done. For steady rates, that equals the ratio of their rates (reciprocal of times). Once the ratio is known, multiply by total wages to get each share. Given Data / Assumptions: A’s time = 3 days ⇒ rate = 1/3 B’s time = 2 days ⇒ rate = 1/2 Total wages = ₹ 225 Concept / Approach:Wage ratio A:B = (1/3):(1/2) = 2:3. A’s share is 2/(2+3) of the total wages. Step-by-Step Solution:Total ratio parts = 2 + 3 = 5A’s share = 2/5 * 225 = ₹ 90 Verification / Alternative check:B’s share = 3/5 * 225 = ₹ 135; together ₹ 225. Why Other Options Are Wrong:₹ 75, ₹ 95, and ₹ 65 do not match the 2:3 split; ₹ 100 is not a 2/5 fraction of 225. Common Pitfalls:Using times (3:2) directly instead of reciprocal rates (2:3). Final Answer:₹ 90

Question 5

Work and Wages – Contract of ₹ 1100 with partial work share known: P, Q, and R take a job for ₹ 1100. P and Q together are supposed to do 7/22 of the work. How much should R receive?

Accepted Answer

Introduction / Context:Lump-sum contracts are split by fractional contributions to total work. If a group’s share of work is known, the remainder belongs to the other party, who then earns the corresponding share of the payment. Given Data / Assumptions: Total payment = ₹ 1100 P + Q together do 7/22 of the work R does the remainder Concept / Approach:R’s work fraction = 1 − 7/22 = 15/22. Therefore, R’s money share is the same fraction of the total amount. Step-by-Step Solution:R’s share = (15/22) * 1100 = 15 * 50 = ₹ 750 Verification / Alternative check:P+Q’s share would be (7/22)*1100 = ₹ 350. Sum: ₹ 350 + ₹ 750 = ₹ 1100. Why Other Options Are Wrong:₹ 350 is P+Q’s combined share, not R’s; other values do not match 15/22 of ₹ 1100. Common Pitfalls:Confusing “P and Q are supposed to do 7/22” with “they did 7/22 of the time”; here we split money by work fractions. Final Answer:₹ 750

Question 6

Work and Wages – Divide $450 among A, B, C by actual work done: A finishes in 10 days, B in 15 days; they work together for 5 days. C completes the remainder in 2 days. Split the $450 payment fairly.

Accepted Answer

Introduction / Context:When workers contribute different fractions of the total job, payment should be split in direct proportion to the work each performs. We compute the work done by A and B in the joint period, determine the remainder, and assign it to C. Given Data / Assumptions: A’s time = 10 days ⇒ rate = 1/10 B’s time = 15 days ⇒ rate = 1/15 They work together for 5 days C completes the rest in 2 days Total payment = $450 Concept / Approach:Total work units are convenient; however, directly using fractions suffices. Joint daily rate of A and B is 1/10 + 1/15 = 1/6, so in 5 days they complete 5/6. The remaining 1/6 is done by C. Split $450 in the ratio 1/2 : 1/3 : 1/6 for A : B : C. Step-by-Step Solution:A’s share of work = 5 * (1/10) = 1/2B’s share of work = 5 * (1/15) = 1/3C’s share of work = 1/6Convert to parts: (3 : 2 : 1). Total parts = 6.Shares: A = 3/6 * 450 = $225; B = 2/6 * 450 = $150; C = 1/6 * 450 = $75 Verification / Alternative check:Sum $225 + $150 + $75 = $450; fractions add to 1. Why Other Options Are Wrong:Other splits do not match the precise 3:2:1 ratio dictated by actual work. Common Pitfalls:Splitting only by rates without accounting for the different time each person actually worked. Final Answer:$225, $150, $75

Question 7

Work and Wages – B’s share when A and B finish together: Individually A needs 30 days and B needs 40 days to complete a job. They finish together and receive $2100. What is B’s share?

Accepted Answer

Introduction / Context:For constant-rate workers, wage shares are proportional to their work rates. Since both worked for the same time together, use rates directly to split the total payment. Given Data / Assumptions: A’s time = 30 days ⇒ rate = 1/30 B’s time = 40 days ⇒ rate = 1/40 Total payment = $2100 Concept / Approach:Ratio A:B = (1/30):(1/40) = 40:30 = 4:3. Thus B’s share is 3/7 of the total. Step-by-Step Solution:Total ratio parts = 4 + 3 = 7B’s share = 3/7 * 2100 = $900 Verification / Alternative check:A’s share = 4/7 * 2100 = $1200; together $2100. Why Other Options Are Wrong:$1200 is A’s share; $800, $1300, and $750 do not equal 3/7 of $2100. Common Pitfalls:Using time ratio 30:40 directly; always use rate ratio (reciprocals). Final Answer:$900

Question 8

Work and Wages – B’s fair share from a contracted amount: A can do the work in 8 days and takes a $320 contract. With B’s help the job finishes in 6 days. What is B’s share of the $320?

Accepted Answer

Introduction / Context:When a contractor hires help, the fair split of the fixed amount is proportional to the actual work contributed by each person. We compute how much of the job A completed in 6 days and assign the remainder to B. Given Data / Assumptions: A’s solo time = 8 days ⇒ A’s rate = 1/8 job/day Actual completion time with B = 6 days Total contract amount = $320 Concept / Approach:Work done by A in 6 days = 6 * (1/8) = 3/4 of the job. Therefore B must have done the remaining 1/4. Payment is split 3/4 to A and 1/4 to B. Step-by-Step Solution:A’s contribution = 3/4 of jobB’s contribution = 1/4 of jobB’s share = 1/4 * $320 = $80 Verification / Alternative check:A’s share = 3/4 * $320 = $240; sum $240 + $80 = $320. Why Other Options Are Wrong:$120 and $100 overpay B; $60 underpays; $240 is A’s share. Common Pitfalls:Splitting by days worked instead of fraction of total job accomplished. Final Answer:$80

Question 9

Work and wages proportionality: If a team of 6 persons working 8 hours per day earns $8400 in one week (same number of working days), then assuming earnings are directly proportional to total person-hours, how much will be earned in a week when 9 pe…

Accepted Answer

Introduction / Context: This question checks proportional reasoning in work-and-wages. When the pay rate per person-hour is constant and the number of working days in the week is the same for both cases, total weekly earnings are proportional to the product of the number of persons and the daily hours they work. Given Data / Assumptions: Case 1: 6 persons, 8 hours/day, weekly earning = $8400. Case 2: 9 persons, 6 hours/day, weekly earning = unknown. Number of working days in the week is the same in both situations. Pay rate per person-hour is unchanged. Concept / Approach: If rate per person-hour is constant and days are equal, earnings scale with person-hours/day. So Earnings_2 / Earnings_1 = (Persons_2 * Hours_2) / (Persons_1 * Hours_1). Compute this ratio and multiply by the first week’s earnings to get the second week’s amount. Step-by-Step Solution: Base person-hours/day (Case 1) = 6 * 8 = 48.New person-hours/day (Case 2) = 9 * 6 = 54.Scaling factor = 54 / 48 = 1.125.New weekly earnings = 8400 * 1.125 = 9450. Verification / Alternative check: Any common factor in working days cancels from both cases: only persons * hours/day matters. The factor 1.125 converts $8400 to $9450 exactly. Why Other Options Are Wrong: $16800 and $16200 imply much higher person-hours than given. $8400 assumes no change. $9000 is an arbitrary nearby figure not matching the precise ratio. Common Pitfalls: Forgetting that both scenarios cover equal numbers of days; using hours rather than person-hours; or assuming linearity with only persons or only hours. Final Answer: $9450

Question 10

Contract sharing with a helper: Three persons take a job for $1200. Their individual times are 8 days, 12 days, and 16 days. With the help of a fourth person, they finish the entire job in 3 days. Find the fair payment (share) for the fourth person.

Accepted Answer

Introduction / Context: In mixed-time work problems, payments are proportional to the actual work done. Given individual capacities (days to complete alone), we can convert to daily work rates, add the fourth person’s unknown rate, and use the total time to finish to determine the helper’s contribution and hence his share of the money. Given Data / Assumptions: Total contract amount = $1200. Worker A alone: 8 days ⇒ rate = 1/8 job/day. Worker B alone: 12 days ⇒ rate = 1/12 job/day. Worker C alone: 16 days ⇒ rate = 1/16 job/day. All four together finish in 3 days. Shares are proportional to individual work done. Concept / Approach: Let the fourth person’s daily rate be x. Total daily rate = 1/8 + 1/12 + 1/16 + x. Over 3 days, total work equals 1 job. Solve for x. Then compute the fourth person’s fraction of the job completed and multiply by $1200 to get his share. Step-by-Step Solution: Known daily rate sum = 1/8 + 1/12 + 1/16 = (6 + 4 + 3)/48 = 13/48.Total work in 3 days: (13/48 + x) * 3 = 1 ⇒ 13/16 + 3x = 1.3x = 1 − 13/16 = 3/16 ⇒ x = 1/16 job/day.Fourth person’s work in 3 days = 3 * (1/16) = 3/16 of the job.Share = (3/16) * 1200 = $225. Verification / Alternative check: The other three together provide 13/48 per day; adding 1/16 gives 16/48 = 1/3 per day; in 3 days, they complete exactly 1 job. Why Other Options Are Wrong: $200 and $180 undervalue the helper’s exact fraction; $250 overstates it; $240 is not aligned with 3/16 of $1200. Common Pitfalls: Splitting money by days participated rather than actual work fractions, or mis-adding the reciprocals. Final Answer: $225

Question 11

DVD rent split by usage time: Samiara, Mahira, and Kiara jointly rent DVDs for ₹ 578. They use them for 8 hours, 12 hours, and 14 hours respectively. Assuming rent is shared in proportion to hours of use, what is Kiara’s share?

Accepted Answer

Introduction / Context: When a common resource is rented and used unevenly, a common fair-division rule is to split the rent in proportion to each person’s usage time. This question applies that idea to three friends renting DVDs together for a fixed fee. Given Data / Assumptions: Total rent = ₹ 578. Usage times: 8 h (Samiara), 12 h (Mahira), 14 h (Kiara). Rent is split proportional to usage hours. Concept / Approach: Let the shares be proportional to 8 : 12 : 14. Reduce the ratio to its simplest terms to make arithmetic easier, sum the parts, and then allocate the total rent according to each person’s part share. Kiara’s share corresponds to the last term of the ratio after reduction. Step-by-Step Solution: Usage ratio = 8 : 12 : 14 = 4 : 6 : 7 (dividing by 2).Sum of parts = 4 + 6 + 7 = 17.Value per part = 578 / 17 = 34.Kiara’s share = 7 parts * ₹ 34 = ₹ 238. Verification / Alternative check: Samiara = 4 * 34 = 136; Mahira = 6 * 34 = 204; Kiara = 7 * 34 = 238; Sum = 578, consistent. Why Other Options Are Wrong: ₹ 204 is Mahira’s share, not Kiara’s. ₹ 192 and ₹ 215 do not align with the exact part value 34. ₹ 225 is an arbitrary round figure. Common Pitfalls: Forgetting to reduce ratios or miscomputing the per-part value by not dividing the total correctly. Final Answer: ₹ 238

Question 12

Daily-wage contract with absences: A laborer is engaged for a fixed number of days for ₹ 5750, but due to absences he receives only ₹ 5000. Assuming the same daily wage throughout and integer numbers of paid days, what is the maximum possible daily …

Accepted Answer

Introduction / Context: The laborer had a fixed daily wage for a fixed-length engagement, but earned less due to absences. The daily wage must divide both the full contracted amount and the actually paid amount, since both are integer multiples of a constant daily rate. To maximize the daily wage under these conditions, we use the greatest common divisor (GCD) of the two totals. Given Data / Assumptions: Total contracted pay if fully present = ₹ 5750. Actual paid due to absences = ₹ 5000. Daily wage is constant; number of paid days are integers. Concept / Approach: If daily wage = d, then 5750 = N * d and 5000 = n * d for integers N and n. Therefore d must divide both 5750 and 5000. The maximum possible d is gcd(5750, 5000). Compute the GCD to find the largest feasible daily wage consistent with both totals being multiples of d. Step-by-Step Solution: gcd(5750, 5000) = gcd(5000, 750) since 5750 − 5000 = 750.5000 mod 750 = 500 ⇒ gcd(750, 500) = 250.Thus the maximum daily wage d = ₹ 250.This yields integer day counts: 5750/250 = 23 days; 5000/250 = 20 days. Verification / Alternative check: Any larger daily wage would fail to divide either 5750 or 5000; any smaller common divisor is possible but not maximal. Why Other Options Are Wrong: ₹ 500 and ₹ 375 do not divide both totals; ₹ 125 divides both but is not the maximum; ₹ 200 is not a common divisor of 5750. Common Pitfalls: Treating the problem as a percentage deduction question rather than a divisibility constraint on a constant daily rate. Final Answer: ₹ 250

Question 13

Wage sharing by efficiency: A completes a job in 12 days and B in 16 days. Working together they earn ₹ 2100. Divide the money fairly in proportion to work done by A and B.

Accepted Answer

Introduction / Context: When multiple workers collaborate, a fair division of payment is proportional to each one’s contribution. For constant daily work rates, contribution is proportional to their rates, which are reciprocals of the individual completion times for the same job. Given Data / Assumptions: A alone: 12 days ⇒ rate = 1/12 job/day. B alone: 16 days ⇒ rate = 1/16 job/day. Total payment = ₹ 2100; equal working duration. Concept / Approach: For a full job completed together, shares are in the ratio of rates 1/12 : 1/16 which simplifies to 16 : 12 = 4 : 3. Divide the total accordingly to get each worker’s fair compensation. Step-by-Step Solution: Rate ratio A : B = 1/12 : 1/16 = 16 : 12 = 4 : 3.Total parts = 4 + 3 = 7.A’s share = 4/7 * 2100 = ₹ 1200.B’s share = 3/7 * 2100 = ₹ 900. Verification / Alternative check: The proportional-split method is equivalent to allocating wages by actual work done in any equal time interval, since work done is rate * time. Why Other Options Are Wrong: The other splits do not reflect the 4:3 ratio implied by 12 vs 16 days; “None” is unnecessary because a valid split exists. Common Pitfalls: Dividing equally or using time ratios directly instead of rate ratios (remember, rate is inverse of time). Final Answer: ₹ 1200 to A, ₹ 900 to B

Question 14

Staggered teamwork and fair pay: A can finish a job in 20 days. After A works alone for 5 days, B joins and together they finish in the next 10 days. If they are paid ₹ 1600 in total, what is the fair payment to A and to B?

Accepted Answer

Introduction / Context: When workers join at different times, the proper division of payment uses the actual fraction of work each one completes. Compute each worker’s contribution from their rates and the periods they worked, then split the total payment in that ratio. Given Data / Assumptions: A alone can finish in 20 days ⇒ A’s rate = 1/20 job/day. A works alone for 5 days, then A and B work together for 10 more days. Total payment = ₹ 1600; shares proportional to work done. Concept / Approach: Find the combined rate during the last 10 days from the fact that the total job is completed in 15 days. From that, extract B’s rate. Then compute A’s total contribution (first 5 days alone plus A’s share during the joint 10 days) and B’s contribution. Divide ₹ 1600 in that ratio. Step-by-Step Solution: Work done by A in first 5 days = 5 * (1/20) = 1/4 of the job.Remaining work = 3/4, finished in 10 days ⇒ combined rate (A + B) = (3/4)/10 = 3/40 job/day.A’s rate = 1/20 = 2/40 ⇒ B’s rate = 3/40 − 2/40 = 1/40 job/day.A’s total work = 1/4 + 10*(1/20) = 1/4 + 1/2 = 3/4; B’s work = 1/4.Payment split = 3/4 : 1/4 = 3 : 1 ⇒ A = ₹ 1200, B = ₹ 400. Verification / Alternative check: A:B = 3:1 indeed sums to ₹ 1600 and matches computed contributions. Why Other Options Are Wrong: Other splits do not reflect the 3:1 work division. “None” is unnecessary because the correct split is determinable. Common Pitfalls: Dividing payment by time spent together only, ignoring A’s solo work; or assuming equal split during the joint period without considering rates. Final Answer: ₹ 1200 to A, ₹ 400 to B

Question 15

Three-worker contract sharing: A, B, and C agree to do a job for ₹ 4200. Their individual times are 6 days, 10 days, and 12 days respectively. If all three work together, what are the fair shares of A, B, and C from ₹ 4200?

Accepted Answer

Introduction / Context: For workers collaborating on a fixed-price job, payment is split proportional to work done, which in turn is proportional to each worker’s constant daily rate. Rates are reciprocals of their individual completion times for the same job. Given Data / Assumptions: A alone: 6 days ⇒ rate = 1/6. B alone: 10 days ⇒ rate = 1/10. C alone: 12 days ⇒ rate = 1/12. Total payment = ₹ 4200; equal working duration together. Concept / Approach: Compute the rate ratio, convert to integer parts, and then divide the total payment accordingly. Using a common denominator helps to avoid fractional parts. Step-by-Step Solution: Using denominator 60: A : B : C = 10 : 6 : 5 (since 1/6, 1/10, 1/12 ⇒ 10/60, 6/60, 5/60).Sum of parts = 10 + 6 + 5 = 21.A’s share = 10/21 * 4200 = ₹ 2000.B’s share = 6/21 * 4200 = ₹ 1200.C’s share = 5/21 * 4200 = ₹ 1000. Verification / Alternative check: The shares add to ₹ 4200 and respect the relative productivities. Why Other Options Are Wrong: Only the option with (₹ 2000, ₹ 1200, ₹ 1000) matches the exact 10:6:5 ratio derived from the given times. Common Pitfalls: Using days as the ratio rather than rates; remember the faster worker gets more due to higher rate. Final Answer: ₹ 2000, ₹ 1200, ₹ 1000

Question 16

Men and women wage comparison via work rates: 2 men + 1 woman finish a job in 14 days; 2 men + 4 women finish the same job in 8 days. If a man earns ₹ 60 per day, what should a woman be paid per day so that wages are proportional to productivity?

Accepted Answer

Introduction / Context: When determining fair daily wages for different worker categories, the wage should reflect relative productivity. By comparing completion times for different team compositions, we can deduce each category’s daily work rate and then set pay accordingly. Given Data / Assumptions: (2m + 1w)*14 = 1 job ⇒ 2m + w = 1/14. (2m + 4w)*8 = 1 job ⇒ 2m + 4w = 1/8. Man’s daily wage = ₹ 60; wages proportional to rate. Concept / Approach: Solve the linear system for m (man’s daily rate) and w (woman’s daily rate). Once w/m is known, multiply by ₹ 60 to get the woman’s fair daily wage. Step-by-Step Solution: From 2m + w = 1/14 and 2m + 4w = 1/8.Subtract: (2m + 4w) − (2m + w) = 3w = 1/8 − 1/14 = 3/56 ⇒ w = 1/56.Then 2m = 1/14 − 1/56 = 3/56 ⇒ m = 3/112.Rate ratio w/m = (1/56) / (3/112) = 2/3.Woman’s daily wage = (2/3) * ₹ 60 = ₹ 40. Verification / Alternative check: Check team rates: 2m + w = 2*(3/112) + 1/56 = 6/112 + 2/112 = 8/112 = 1/14; similarly 2m + 4w = 6/112 + 4/56 = 6/112 + 8/112 = 14/112 = 1/8. Why Other Options Are Wrong: ₹ 30 and ₹ 35 undervalue productivity; ₹ 50 overpays relative to the solved rate; ₹ 45 is not supported by the linear system. Common Pitfalls: Dividing total days instead of solving the system, or equating wages to time rather than rate. Final Answer: ₹ 40

Question 17

Three-worker job for ₹ 1110: A, B, and C finish alone in 12, 15, and 18 days respectively. If they share the proceeds fairly according to work done, what amount does C receive?

Accepted Answer

Introduction / Context: Payment splitting among different rate workers is proportional to their rates, which are reciprocals of completion times. This problem asks specifically for the third worker’s share after all three work together on a fixed-price job. Given Data / Assumptions: A: 12 days ⇒ rate = 1/12. B: 15 days ⇒ rate = 1/15. C: 18 days ⇒ rate = 1/18. Total payment = ₹ 1110; working together for equal time. Concept / Approach: Shares are proportional to the rates 1/12 : 1/15 : 1/18. Use a common denominator (e.g., 180) to convert to integer parts and then allocate the total amount based on those parts. The question asks for C’s amount only. Step-by-Step Solution: Rates → parts using 180: A = 15, B = 12, C = 10.Total parts = 15 + 12 + 10 = 37.C’s share = 10/37 * 1110 = 300. Verification / Alternative check: A: 15/37 * 1110 = 450; B: 12/37 * 1110 = 360; C: 300; sum = 1110. Why Other Options Are Wrong: ₹ 275, ₹ 335, and ₹ 339 do not match 10/37 of ₹ 1110; ₹ 320 is also off. Common Pitfalls: Using days directly instead of rates; always transform to rates before splitting. Final Answer: ₹ 300

Question 18

Man–boy combined wages: A man and a boy together earn ₹ 800 for 5 days. The man’s efficiency is three times the boy’s. What is the boy’s daily wage if pay is proportional to work done?

Accepted Answer

Introduction / Context: When two workers have known relative efficiencies and work for the same time, their wage split should match their relative work contributions. From the total payment over 5 days, we can deduce the boy’s 5-day share and then his daily wage. Given Data / Assumptions: Total pay for 5 days together = ₹ 800. Man’s efficiency = 3 × boy’s efficiency. Payment proportional to work contributed. Concept / Approach: Let the boy’s one-day work be 1 unit; then the man’s is 3 units. Together they produce 4 units per day. Over 5 days they produce 20 units. Split ₹ 800 in the ratio 3:1 per day, which is the same as 15:5 over 5 days. The boy receives one-fourth of the total because he contributes 1 out of 4 units each day. Step-by-Step Solution: Work ratio per day = Man : Boy = 3 : 1.Wage ratio for 5 days is also 3 : 1.Boy’s share for 5 days = 1/4 * 800 = ₹ 200.Boy’s daily wage = 200 / 5 = ₹ 40. Verification / Alternative check: Man’s 5-day share = 600 ⇒ daily = 120; 120 is exactly three times 40, consistent with the efficiency ratio. Why Other Options Are Wrong: ₹ 56 and ₹ 44 overvalue; ₹ 76 is unrelated; ₹ 60 conflicts with the 3:1 efficiency ratio when combined with boy’s daily rate. Common Pitfalls: Splitting ₹ 800 equally or forgetting to divide the boy’s 5-day share by 5 to get the daily wage. Final Answer: ₹ 40

Question 19

Two-worker collaboration payment: A alone completes a job in 15 days; A and B together complete it in 10 days. If the total payment is ₹ 1500, how should it be divided between A and B in proportion to their work?

Accepted Answer

Introduction / Context: This is a standard “find B’s rate from joint rate” problem. Once each worker’s rate is known, their contributions over the same time interval can be compared, and the payment divided proportionally to those contributions for the full job completed together. Given Data / Assumptions: A alone: 15 days ⇒ rate_A = 1/15. A + B: 10 days ⇒ rate_(A+B) = 1/10. Total payment = ₹ 1500; both worked simultaneously for the whole job. Concept / Approach: B’s rate = rate_(A+B) − rate_A = 1/10 − 1/15. Shares for the full job are proportional to rates (since the time they worked together is the same for both). Compute the ratio and split the money accordingly. Step-by-Step Solution: rate_B = 1/10 − 1/15 = (3 − 2)/30 = 1/30.Rate ratio A : B = 1/15 : 1/30 = 2 : 1.A’s share = 2/3 * 1500 = ₹ 1000.B’s share = 1/3 * 1500 = ₹ 500. Verification / Alternative check: The 2:1 split matches the fact that A works twice as fast as B. Why Other Options Are Wrong: Equal split (₹ 750 each) ignores different efficiencies; other splits do not match the 2:1 ratio. Common Pitfalls: Subtracting days instead of rates; always subtract rates to find the missing worker’s rate. Final Answer: ₹ 1000 to A, ₹ 500 to B

Question 20

Remainder of work done by C: A, B, and C agree to do a job for ₹ 480. A and B together complete 5/8 of the work; C alone completes the rest. How much should C receive?

Accepted Answer

Introduction / Context: When parts of a job are clearly assigned, the money is fairly split by the fractions of the job each party completes. Here, A and B together do a known portion, and C does the remainder alone; therefore, C’s share is that remainder fraction of the total payment. Given Data / Assumptions: Total job price = ₹ 480. A and B together do 5/8 of the job. C alone does the remainder 3/8 of the job. Concept / Approach: Since C’s work fraction is 3/8 of the whole job, C’s share is 3/8 of the total payment. No rate calculation is required because the fraction is given directly. Step-by-Step Solution: C’s job fraction = 1 − 5/8 = 3/8.C’s share = (3/8) * ₹ 480 = ₹ 180. Verification / Alternative check: A and B together would then share ₹ 300, which is 5/8 of ₹ 480, consistent with the given breakdown. Why Other Options Are Wrong: ₹ 177 and ₹ 150 are not equal to 3/8 of ₹ 480; “None” is unnecessary; ₹ 210 corresponds to 7/16, not applicable here. Common Pitfalls: Overcomplicating by searching for rates; with explicit fractions, the split is direct. Final Answer: ₹ 180

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