Question 1

Man–boy wages with 6:1 efficiency: A man and a boy earn ₹ 1400 for 10 days of joint work. If the man’s efficiency is six times the boy’s and wages are proportional to work done, what is the boy’s daily wage?

Accepted Answer

Introduction / Context: Relative efficiency determines how total pay should be split among workers who work together for equal time. Once the boy’s total share over 10 days is found from the ratio, the daily wage is the share divided by 10. Given Data / Assumptions: Total pay for 10 days together = ₹ 1400. Efficiency ratio (man : boy) = 6 : 1. Wages proportional to work done. Concept / Approach: With efficiency 6:1, the wage ratio is also 6:1. Thus the boy’s fraction is 1/7 of the total. Compute the boy’s 10-day share and divide by 10 to get his daily wage. Step-by-Step Solution: Total parts = 6 + 1 = 7.Boy’s 10-day share = 1/7 * 1400 = ₹ 200.Boy’s daily wage = 200 / 10 = ₹ 20. Verification / Alternative check: Man’s daily wage would then be 6 times ₹ 20 = ₹ 120. Over 10 days: ₹ 1200; plus boy’s ₹ 200 equals ₹ 1400 total. Why Other Options Are Wrong: ₹ 10 and ₹ 15 are too low; ₹ 30 and ₹ 25 are too high given the exact 6:1 ratio and total amount. Common Pitfalls: Splitting equally or forgetting to divide the boy’s multi-day share by the number of days. Final Answer: ₹ 20

Question 2

Two-worker payment from rates: A completes a job in 3 days, B in 4 days. They work together and receive ₹ 2800 in total. How much should A receive, if the split is proportional to work done?

Accepted Answer

Introduction / Context: A and B have constant daily rates inversely proportional to their completion times. When they complete the job together, the fair split of wages is proportional to their rates, since both contributed for the same duration to finish the job once. Given Data / Assumptions: A: 3 days ⇒ rate = 1/3. B: 4 days ⇒ rate = 1/4. Total payment = ₹ 2800. Concept / Approach: Split by rates: A : B = 1/3 : 1/4. Convert to a simple integer ratio and apply it to the total payment to find A’s share precisely. Step-by-Step Solution: A : B = 1/3 : 1/4 = 4 : 3.Total parts = 4 + 3 = 7.A’s share = 4/7 * 2800 = ₹ 1600. Verification / Alternative check: B’s share = 3/7 * 2800 = ₹ 1200; sums to ₹ 2800 and matches the 4:3 rate ratio. Why Other Options Are Wrong: ₹ 1900, ₹ 1300, ₹ 1400, and ₹ 1200 do not reflect the 4/7 fraction for A. Common Pitfalls: Averaging days or wages instead of using the correct reciprocal relationship of days and rates. Final Answer: ₹ 1600

Question 3

Comparing wages by speed: Worker 1 can finish in 26 days and Worker 2 in 39 days. If they work together on the same job, by what percentage are the wages of the first worker more than those of the second (assuming pay proportional to work done)?

Accepted Answer

Introduction / Context: When two workers collaborate and are paid by contribution, their wage ratio equals their rate ratio. Since rate is the reciprocal of days to finish alone, a quicker worker earns more. The question asks for the percentage by which the first worker’s wages exceed the second’s when both work the same time on the same job. Given Data / Assumptions: Worker 1 alone: 26 days ⇒ rate r1 = 1/26. Worker 2 alone: 39 days ⇒ rate r2 = 1/39. Wages proportional to rate (same time worked). Concept / Approach: Wage ratio r1 : r2 = 1/26 : 1/39 = 39 : 26, which simplifies to 3 : 2. The percent by which the first exceeds the second is ((3 − 2)/2) * 100 = 50% more. Step-by-Step Solution: Compute ratio: (1/26) / (1/39) = 39/26 = 3/2.Wage ratio = 3 : 2.Excess percentage = (difference / second) * 100 = (1/2) * 100 = 50%. Verification / Alternative check: If second earns ₹ 200, first earns ₹ 300; the increase is ₹ 100 over ₹ 200 ⇒ 50%. Why Other Options Are Wrong: 25%, 35%, 15%, and 20% do not match the exact 3:2 ratio. Common Pitfalls: Computing percentage of the total rather than relative to the second worker’s wage. Final Answer: 50%

Question 4

Finding 20% of A’s share: A alone can finish a job in 2 days; B alone in 3 days. They work together on a job for a total wage of ₹ 6000. What is 20% of A’s fair share?

Accepted Answer

Introduction / Context: Shares for two workers with known individual completion times are proportional to their rates. After computing A’s correct share from the total, take 20% of that amount as requested by the problem statement. Given Data / Assumptions: A alone: 2 days ⇒ rate_A = 1/2. B alone: 3 days ⇒ rate_B = 1/3. Total wage for the job = ₹ 6000. Concept / Approach: Wage split ratio A : B = 1/2 : 1/3 = 3 : 2. Hence A’s share is 3/5 of the total. Then compute 20% of that amount to answer the question precisely. Step-by-Step Solution: A : B = 3 : 2 ⇒ A’s share = 3/5 * 6000 = ₹ 3600.20% of A’s share = 0.20 * 3600 = ₹ 720. Verification / Alternative check: B’s share would be ₹ 2400; the total still sums to ₹ 6000, consistent with the 3:2 ratio. Why Other Options Are Wrong: ₹ 350, ₹ 420, and ₹ 600 do not equal 20% of ₹ 3600; ₹ 820 is arbitrary here. Common Pitfalls: Taking 20% of the total instead of A’s share; or inverting the ratio from times rather than rates. Final Answer: ₹ 720

Question 5

Two-person collaboration: Vandana completes the work in 10 days alone; with Ruchi, the work finishes in 6 days. If they earn ₹ 200 for the job, what is Ruchi’s fair share?

Accepted Answer

Introduction / Context: When one worker’s solo time and the combined time are known, we can find the second worker’s rate by subtracting rates. Payment for the joint job is split according to the ratio of their rates (equivalently, their contributed fractions of the job). Given Data / Assumptions: Vandana alone: 10 days ⇒ rate_V = 1/10. Vandana + Ruchi together: 6 days ⇒ rate_(V+R) = 1/6. Total payment = ₹ 200; wages proportional to work done. Concept / Approach: Ruchi’s rate = 1/6 − 1/10. Then compute the ratio of Vandana’s to Ruchi’s rates to split the payment. Finally, apply the ratio to ₹ 200 to extract Ruchi’s share. Step-by-Step Solution: rate_R = 1/6 − 1/10 = (5 − 3)/30 = 2/30 = 1/15.Rate ratio V : R = 1/10 : 1/15 = 3 : 2.Ruchi’s share = 2/5 * 200 = ₹ 80. Verification / Alternative check: Vandana’s share would be ₹ 120 (3/5 of ₹ 200); the sum is ₹ 200 and matches the 3:2 ratio. Why Other Options Are Wrong: ₹ 100, ₹ 60, and ₹ 75 do not equal 2/5 of ₹ 200; ₹ 120 is Vandana’s share, not Ruchi’s. Common Pitfalls: Subtracting days instead of rates, or splitting equally despite different speeds. Final Answer: ₹ 80

Question 6

Money good for separate wages: The same sum pays A’s wages for 21 days or B’s wages for 28 days. For how many days will it pay both A and B together if both are paid daily and the entire sum is used?

Accepted Answer

Introduction / Context: If a fixed sum can pay one worker for a certain duration and another for a different duration, the daily wages are inversely related to those durations. To find how long the same sum can pay both together, compute the combined daily outlay and divide the total sum by that outlay. Given Data / Assumptions: The sum equals 21 days of A’s wage or 28 days of B’s wage. Daily wages are constant for each worker. All payments are made daily; both work together the entire time. Concept / Approach: Let A’s daily wage be a and B’s be b. Then 21a = 28b = total sum M. Use the relation a/b = 28/21 = 4/3. Compute M/(a + b) to get the number of days the same sum sustains both together. Step-by-Step Solution: Let a = 4k and b = 3k (from a/b = 4/3).Total sum M = 21a = 21*4k = 84k.Combined daily outlay (a + b) = 7k.Days payable = M / (a + b) = 84k / 7k = 12 days. Verification / Alternative check: Alternatively use harmonic manipulation: 1/Days = 1/21 + 1/28 = (4 + 3)/84 = 7/84 ⇒ Days = 12. Why Other Options Are Wrong: 24 1/2 and 14 ignore combined outlay; 12 1/4 is close but incorrect; 10 1/2 does not fit the precise ratio. Common Pitfalls: Averaging 21 and 28 instead of using reciprocal relationships or not converting to daily outlay correctly. Final Answer: 12 days

Question 7

Three workers together: Amit, Vipul, and Kapil complete a job in 12, 16, and 24 days respectively. If they earn ₹ 2700 for the job, what is Vipul’s share under a fair division?

Accepted Answer

Introduction / Context: For three workers with different individual completion times, their rates determine their shares in a combined job. The fair split is proportional to rates, i.e., inverses of their days to finish alone. Given Data / Assumptions: Amit: 12 days ⇒ rate = 1/12. Vipul: 16 days ⇒ rate = 1/16. Kapil: 24 days ⇒ rate = 1/24. Total payment = ₹ 2700. Concept / Approach: Convert rates to integer parts using a common denominator (e.g., 48): 4, 3, and 2 parts respectively. Vipul’s share corresponds to 3 out of the total (4 + 3 + 2) = 9 parts of the payment. Step-by-Step Solution: Parts: Amit 4, Vipul 3, Kapil 2 (denominator 48).Sum of parts = 9.Vipul’s share = 3/9 * 2700 = ₹ 900. Verification / Alternative check: Amit’s share = 4/9 * 2700 = 1200; Kapil’s share = 2/9 * 2700 = 600; sums to ₹ 2700. Why Other Options Are Wrong: ₹ 450 and ₹ 225 are too small (half or quarter of the correct value). ₹ 1000 and ₹ 800 do not match the exact 3/9 fraction. Common Pitfalls: Using days instead of rates; always invert days to get parts for fair division. Final Answer: ₹ 900

Question 8

Daily wages with different days worked: A, B, and C complete a work costing ₹ 1800. They work for 6, 4, and 9 days respectively, and their daily wage rates are in the ratio 5 : 6 : 4. How much should A receive?

Accepted Answer

Introduction / Context: When workers have different daily wage rates and work for different numbers of days, their total payments are proportional to (daily rate) * (days worked). With the cost of the work fixed, divide the total amount in this compound proportion to determine each person’s due amount. Given Data / Assumptions: Daily wage ratio A : B : C = 5 : 6 : 4. Days worked A = 6, B = 4, C = 9. Total payment = ₹ 1800. Concept / Approach: Compute proportional “earnings units” as (rate factor) * (days). Sum across all three to get total units, then allocate the ₹ 1800 according to each worker’s units. A’s amount is what is requested. Step-by-Step Solution: A-units = 5 * 6 = 30.B-units = 6 * 4 = 24.C-units = 4 * 9 = 36.Total units = 30 + 24 + 36 = 90.Value per unit = 1800 / 90 = ₹ 20.A’s amount = 30 * 20 = ₹ 600. Verification / Alternative check: B’s amount = 24 * 20 = ₹ 480; C’s = 36 * 20 = ₹ 720; total = ₹ 1800. Why Other Options Are Wrong: ₹ 500, ₹ 450, and ₹ 700 do not equal 30 units at ₹ 20 per unit; ₹ 900 is too high given the unit breakdown. Common Pitfalls: Dividing simply by days or by the rate ratio alone; the correct approach multiplies both factors. Final Answer: ₹ 600

Question 9

Work and wages sharing: A and B undertake a piece of work for a total payment of ₹ 1200. A alone can finish the work in 8 days, and B alone can finish it in 6 days. With the additional help of C, the job is completed in 3 days. Based on individual w…

Accepted Answer

Introduction / Context: This is a classic work-and-wages allocation problem. When multiple people work together for a lump-sum amount, the distribution of money must be proportional to the amount of work each person actually does. We are given individual times (A: 8 days, B: 6 days) and the joint completion time with C (3 days). The target is C's share from ₹ 1200. Given Data / Assumptions: Total job = 1 unit of work Rate(A) = 1/8 job per day Rate(B) = 1/6 job per day With C, job completes in 3 days ⇒ combined rate = 1/3 job per day Total payment to be divided = ₹ 1200 Concept / Approach: Find C's daily rate by subtracting A and B's combined rate from the overall rate. Then compute the work C completes during 3 days. Finally, allocate the total amount in proportion to work done. Only C's portion is requested here. Step-by-Step Solution: Combined rate (A+B+C) = 1/3Rate(A) + Rate(B) = 1/8 + 1/6 = (3 + 4) / 24 = 7/24Rate(C) = 1/3 − 7/24 = 8/24 − 7/24 = 1/24 job per dayWork by C in 3 days = 3 * (1/24) = 1/8 of the jobC's share = 1/8 * ₹ 1200 = ₹ 150 Verification / Alternative check: Shares by fraction: A's work = 3*(1/8) = 3/8; B's work = 3*(1/6) = 1/2; C's work = 1/8. Sum = 3/8 + 1/2 + 1/8 = 1 (consistent). Money division would be ₹ 450, ₹ 600, ₹ 150 respectively, summing to ₹ 1200. Why Other Options Are Wrong: ₹ 450 or ₹ 300 imply C did 3/8 or 1/4 of the work, which contradicts the computed rate.₹ 100 understates C's contribution; he completes exactly 1/8 of the job. Common Pitfalls: Confusing time ratios with work ratios; dividing money by days instead of by work; forgetting to multiply the rate by total working days to get each person's completed fraction. Final Answer: ₹ 150

Question 10

Absence-fine wage puzzle: A worker is hired for a 50-day job with the rule: he earns ₹ 12 for each day worked but is fined ₹ 6 for each day absent. After the job ends, he receives ₹ 420 in net payment. For how many days did he not work?

Accepted Answer

Introduction / Context: This wage question mixes earnings for working days with a penalty for absences. The essential idea is to set up a simple linear expression for the net amount received and then solve for the number of absent days. Given Data / Assumptions: Total scheduled days = 50 Pay per working day = ₹ 12 Fine per absent day = ₹ 6 Net payment received = ₹ 420 Concept / Approach: If the worker is absent for x days, he works for (50 − x) days. Net pay equals earnings for worked days minus fines for absent days. Set that equal to ₹ 420 and solve for x. Step-by-Step Solution: Let x = number of absent daysNet = 12*(50 − x) − 6*x= 600 − 12x − 6x = 600 − 18xGiven net = 420 ⇒ 600 − 18x = 42018x = 180 ⇒ x = 10 Verification / Alternative check: Work days = 40 ⇒ earnings = 40 * 12 = ₹ 480; absent days = 10 ⇒ fine = 10 * 6 = ₹ 60; net = 480 − 60 = ₹ 420, which matches the data. Why Other Options Are Wrong: 15 or 20 days absent would over-deduct, producing net far below ₹ 420.5 days absent would yield ₹ 540 net, which is too high. Common Pitfalls: Adding the fine instead of subtracting; forgetting that working and absent days must sum to 50; arithmetic slips when distributing 12 over (50 − x). Final Answer: 10 days

Question 11

Earnings in joint work: Ram can finish a job alone in 9 days, while Shyam can finish it alone in 15 days. If they work together and share the payment in proportion to their actual work done, in what ratio should their total earnings be divided (Ram …

Accepted Answer

Introduction / Context: Payment in joint work is divided according to the work contributed by each person. When individual times to complete a job are known, their rates (work per day) are inverses of these times. The ratio of rates gives the ratio of earnings for any common working period. Given Data / Assumptions: Time(Ram) = 9 days ⇒ Rate(Ram) = 1/9 job per day Time(Shyam) = 15 days ⇒ Rate(Shyam) = 1/15 job per day They work together for the same duration Concept / Approach: Earnings ratio equals work ratio equals rate ratio for equal time worked. Therefore, divide 1/9 by 1/15 to get the ratio Ram : Shyam. Step-by-Step Solution: Rate ratio = (1/9) : (1/15)= (1/9) * (15/1) = 15/9 = 5/3Hence, Ram : Shyam = 5 : 3 Verification / Alternative check: Consider an LCM of days (45). In 45 days, Ram does 45*(1/9) = 5 jobs; Shyam does 45*(1/15) = 3 jobs. Therefore 5 : 3. Why Other Options Are Wrong: 3 : 5 or 2 : 3 invert or distort the correct rate comparison.'None of these' is unnecessary since 5 : 3 fits perfectly. Common Pitfalls: Confusing time ratios with work ratios. Remember: smaller time means higher rate and larger share. Final Answer: 5 : 3

Question 12

Men–women wage conversion: The wages of 10 women for 5 days total ₹ 1250. The daily wage of a man is twice that of a woman. How many men must work for 8 days to collectively earn ₹ 1600?

Accepted Answer

Introduction / Context: This problem converts between women's and men's wage rates and then scales the workforce to meet a target earning in a given time. The essential tools are unit wage calculation and proportional reasoning. Given Data / Assumptions: Total wages for 10 women over 5 days = ₹ 1250 Therefore, 1 woman per day wage = ? 1 man per day wage = 2 * (1 woman per day wage) Target: men working 8 days must earn ₹ 1600 Concept / Approach: First find the daily wage of a woman, then double it to get the man's daily wage. Finally, compute how many men are needed so that their combined 8-day wage equals ₹ 1600. Step-by-Step Solution: Let w = woman's daily wage10 women for 5 days ⇒ 50w = 1250 ⇒ w = ₹ 25Man's daily wage m = 2w = ₹ 50Let n = number of men. Total in 8 days = n * 8 * 50 = 400n400n = 1600 ⇒ n = 4 Verification / Alternative check: 4 men for 8 days earn 4 * 8 * 50 = ₹ 1600, matching the requirement. Why Other Options Are Wrong: 5, 6, or 7 men would overshoot the target earnings; fewer than 4 would undershoot. Common Pitfalls: Using 10 instead of 50 woman-days in the initial calculation; forgetting to multiply by the number of days when converting to men's wages. Final Answer: 4

Question 13

Proportional wages with different working days: A, B and C agree to complete a job for ₹ 2574. They actually take different spans: A works for 8 days, B for 9 days, and C for 12 days to complete the work. Their daily wage rates are in the ratio 3 : …

Accepted Answer

Introduction / Context: When people work different numbers of days and their daily rates are in a given ratio, the final payment is divided in proportion to (working days) * (daily rate). This converts the ratio into actual weighted shares before splitting the lump sum. Given Data / Assumptions: A, B, C work for 8, 9, 12 days respectively Daily wage ratio A : B : C = 3 : 5 : 4 Total payment to divide = ₹ 2574 Concept / Approach: Let the common daily-rate unit be k. Then daily wages are 3k, 5k, 4k. Multiply by days worked to get individual shares before normalization, add them, and scale to the total amount ₹ 2574. Step-by-Step Solution: A's share weight = 8 * 3k = 24kB's share weight = 9 * 5k = 45kC's share weight = 12 * 4k = 48kTotal weight = 24k + 45k + 48k = 117k117k = ₹ 2574 ⇒ k = 22C's amount = 48k = 48 * 22 = ₹ 1056 Verification / Alternative check: Compute A and B: A = 24*22 = ₹ 528; B = 45*22 = ₹ 990; C = 48*22 = ₹ 1056. Sum = 528 + 990 + 1056 = ₹ 2574, which matches the total. Why Other Options Are Wrong: ₹ 987 or ₹ 1035 or ₹ 1100 do not correspond to the exact 24:45:48 weighted split driven by days and rate ratio. Common Pitfalls: Dividing merely by the 3:5:4 ratio without accounting for unequal working days; neglecting to scale to the given total after finding k. Final Answer: ₹ 1056

Question 14

Three-person job completed in 5 days: A and B agree to complete a work for ₹ 600. A alone can finish in 15 days and B alone in 20 days. With the help of C, they finish in 5 days. Divide the money among A, B and C according to their work contribution…

Accepted Answer

Introduction / Context: When a lump-sum is paid for a task completed jointly, each person's share equals their fraction of the total work. Here, A and B's individual times are given; together with C they finish in 5 days. We will compute each person's contribution and then proportionally divide ₹ 600. Given Data / Assumptions: A's time = 15 days ⇒ rate = 1/15 B's time = 20 days ⇒ rate = 1/20 Finished with C in 5 days ⇒ total rate = 1/5 Total payment = ₹ 600 Concept / Approach: C's rate equals the total rate minus (A + B)'s rate. Then, each share fraction = individual rate / total rate. Multiply this fraction by ₹ 600 to get each person's amount. Step-by-Step Solution: Rate(A) + Rate(B) = 1/15 + 1/20 = 4/60 + 3/60 = 7/60Total rate = 1/5 = 12/60Rate(C) = 12/60 − 7/60 = 5/60 = 1/12Share fractions = (rate)/(1/5) ⇒ A = (1/15)/(1/5) = 1/3; B = (1/20)/(1/5) = 1/4; C = (1/12)/(1/5) = 5/12Amounts: A = 1/3*600 = ₹ 200; B = 1/4*600 = ₹ 150; C = 5/12*600 = ₹ 250 Verification / Alternative check: Fractions sum: 1/3 + 1/4 + 5/12 = 4/12 + 3/12 + 5/12 = 1. Amounts add to ₹ 600. Consistent. Why Other Options Are Wrong: Equal split or other permutations do not match the computed contribution fractions. Common Pitfalls: Multiplying rates by 5 days and then re-normalizing (works too), but forgetting to divide by the total can cause errors. The fraction method is cleaner. Final Answer: 200 , 150 , 250

Question 15

Daily earnings from pairwise totals: A, B and C together earn ₹ 375 in 5 days. A and B together earn ₹ 450 in 10 days. A and C together earn ₹ 200 in 4 days. Determine the daily earning (per day) of each: A, B and C.

Accepted Answer

Introduction / Context: We are given combined earnings over multiple-day periods for different pairs and for all three together. The trick is to convert each total into a per-day figure and then solve the resulting system of linear equations to get individual daily earnings. Given Data / Assumptions: (A+B+C) over 5 days = ₹ 375 ⇒ per day = 75 (A+B) over 10 days = ₹ 450 ⇒ per day = 45 (A+C) over 4 days = ₹ 200 ⇒ per day = 50 Concept / Approach: Let a, b, c be daily earnings. Then we have three equations: a+b+c=75, a+b=45, a+c=50. Subtract to obtain b and c, and then find a. Step-by-Step Solution: a + b + c = 75a + b = 45 ⇒ c = 75 − 45 = 30a + c = 50 ⇒ a = 50 − 30 = 20Then b = 45 − a = 25Hence daily earnings: A = 20, B = 25, C = 30 Verification / Alternative check: Check pairs: A+C = 20+30=50 (matches); A+B = 20+25=45 (matches); A+B+C = 75 (matches). Why Other Options Are Wrong: Other permutations present different assignments and do not satisfy all three equations simultaneously. Common Pitfalls: Forgetting to convert totals to per-day values; algebraic slip when subtracting equations; swapping the identities of b and c. Final Answer: 20 , 25 , 30

Question 16

Mixed men–women wage rates: 5 men and 6 women together earn ₹ 2160 in 4 days; 8 men and 10 women together earn ₹ 4400 in 5 days. In how many days will 4 men and 9 women together earn ₹ 1800?

Accepted Answer

Introduction / Context: We are to determine per-day wages for a man and a woman using two combined scenarios. With those unit rates, we can then compute how long another group will take to earn a specified amount. This is a standard linear system setup. Given Data / Assumptions: (5m + 6w) for 4 days = ₹ 2160 ⇒ per day = 2160/4 = 540 (8m + 10w) for 5 days = ₹ 4400 ⇒ per day = 4400/5 = 880 Find days d so that (4m + 9w) * d = ₹ 1800 Concept / Approach: Let man's daily wage be M and woman's daily wage be W. Solve the linear equations: 5M + 6W = 540 and 8M + 10W = 880. Then compute (4M + 9W) and finally get d = 1800 / (4M + 9W). Step-by-Step Solution: 5M + 6W = 5408M + 10W = 880Solve ⇒ W = 40, M = 604M + 9W = 4*60 + 9*40 = 240 + 360 = 600 per dayDays d = 1800 / 600 = 3 Verification / Alternative check: Back-substitute M and W into original equations to confirm: 5*60 + 6*40 = 540; 8*60 + 10*40 = 880. Both hold true. Why Other Options Are Wrong: 4, 5, 6 days do not match the computed daily earning capacity of 4 men and 9 women. Common Pitfalls: Arithmetic slips in elimination; forgetting to convert totals to per-day figures before forming equations; mixing wages with work rates (here wages are linear, not inverse-time rates). Final Answer: 3

Question 17

Three workers with partial contribution: A can complete a job in 12 days and B can complete it in 15 days. A and B work together for 5 days; the remaining work is done by C alone. If the total wage paid is ₹ 720, what is B's share?

Accepted Answer

Introduction / Context: This problem distributes a fixed payment according to the actual fraction of work completed by each participant. A and B work together for a fixed time; C finishes the remainder. We compute each contribution and then split ₹ 720 proportionally. Given Data / Assumptions: Total job = 1 unit Rate(A) = 1/12, Rate(B) = 1/15 Joint work by A and B for 5 days Remaining work is done by C Total payment = ₹ 720 Concept / Approach: Find work completed by A and B in 5 days; the leftover is C's portion. Convert each portion into money by multiplying each fraction by ₹ 720. B's share is requested. Step-by-Step Solution: Work by A in 5 days = 5 * (1/12) = 5/12Work by B in 5 days = 5 * (1/15) = 1/3Total done by A+B = 5/12 + 1/3 = 5/12 + 4/12 = 3/4Remaining = 1 − 3/4 = 1/4 ⇒ C's workB's share = (1/3) * 720 = ₹ 240 Verification / Alternative check: Convert all shares to money: A = (5/12)*720 = ₹ 300; B = ₹ 240; C = (1/4)*720 = ₹ 180. Sum = ₹ 720 (consistent). Why Other Options Are Wrong: ₹ 95, ₹ 100, ₹ 104 are far below the proportion 1/3 of ₹ 720. Common Pitfalls: Allocating by days rather than by work; forgetting that C's share is solely the leftover portion after A and B's combined effort. Final Answer: ₹ 240

Question 18

Sharing based on work rates: A, B and C can finish a job alone in 15, 20 and 25 days respectively. They work together and earn a total of ₹ 4700. What is C's share if the payment is split in proportion to their work rates?

Accepted Answer

Introduction / Context: When all three work together for the same time, the payment division should follow their work rates (inverse of the individual times). We compute the fraction of the total work rate contributed by C and allocate ₹ 4700 accordingly. Given Data / Assumptions: A: 1/15, B: 1/20, C: 1/25 job per day Total payment = ₹ 4700 All three work concurrently Concept / Approach: C's share fraction = Rate(C) / (Rate(A) + Rate(B) + Rate(C)). Multiply this by the total amount to get C's share in rupees. Step-by-Step Solution: Sum of rates = 1/15 + 1/20 + 1/25 = (20 + 15 + 12) / 300 = 47/300C's fraction = (1/25) / (47/300) = (12/300) / (47/300) = 12/47C's share = 12/47 * 4700 = ₹ 1200 Verification / Alternative check: Note that 47 * 100 = 4700, so 12/47 * 4700 = 12 * 100 = ₹ 1200 directly. Why Other Options Are Wrong: ₹ 1500, ₹ 1800, ₹ 2000 correspond to larger fractions and do not match the calculated 12/47 of the total. Common Pitfalls: Adding times instead of rates; forgetting to normalize by the total of the rates. Final Answer: ₹ 1200

Question 19

Two workers with a helper: Ramesh and Suresh take a job for ₹ 800. Ramesh alone can finish it in 12 days; Suresh alone in 16 days. With the assistance of a boy, they finish in 6 days. How should the money be divided among Ramesh, Suresh, and the boy…

Accepted Answer

Introduction / Context: Lump-sum wage splitting by contribution requires computing each person's share of the total work. The boy's presence speeds up completion to 6 days; from this we infer his effective rate and then split ₹ 800 accordingly. Given Data / Assumptions: Rate(Ramesh) = 1/12 Rate(Suresh) = 1/16 Total rate with boy = 1/6 Total amount = ₹ 800 Concept / Approach: Boy's rate = total rate − (Ramesh + Suresh) rate. Then, each share fraction = rate / total rate. Multiply these fractions by ₹ 800 to determine the payments. Step-by-Step Solution: Rate(R+S) = 1/12 + 1/16 = 4/48 + 3/48 = 7/48Total rate = 1/6 = 8/48Rate(boy) = 8/48 − 7/48 = 1/48Share fractions (multiply by 6): R = 6*(1/12) = 1/2; S = 6*(1/16) = 3/8; Boy = 6*(1/48) = 1/8Payments: R = 1/2*800 = ₹ 400; S = 3/8*800 = ₹ 300; Boy = 1/8*800 = ₹ 100 Verification / Alternative check: Fractions sum to 1; payments sum to ₹ 800 — consistent. Why Other Options Are Wrong: Options that give the boy ₹ 400 or ₹ 100 but mis-allocate others do not match the exact rate-derived fractions. Common Pitfalls: Proportioning by days worked instead of rates; miscomputing the boy's rate by forgetting to subtract both Ramesh and Suresh from the total rate. Final Answer: Ramesh = ₹ 400, Suresh = ₹ 300 and boy = ₹ 100

Question 20

Staggered departures on a contract: A, B and C can do a piece of work in 20, 24 and 30 days respectively. They contract the work for ₹ 5400 and start together, but B leaves 2 days before completion and C leaves 5 days before completion. What is A's …

Accepted Answer

Introduction / Context: Here, not all workers stay for the full duration. We must first determine the total project duration from the staggered participation, then compute each person’s actual work amount. Finally, allocate the fixed ₹ 5400 proportional to these contributions. This mixes rate calculations with timeline reasoning. Given Data / Assumptions: Rate(A) = 1/20; Rate(B) = 1/24; Rate(C) = 1/30 B worked until 2 days before finish C worked until 5 days before finish Total remuneration = ₹ 5400 Concept / Approach: Let total duration = T days. Then total work equals: T/20 + (T − 2)/24 + (T − 5)/30 = 1. Solve for T. Then compute A’s work fraction = T/20 and multiply by ₹ 5400 to get A’s share. Step-by-Step Solution: T/20 + (T − 2)/24 + (T − 5)/30 = 1Use denominator 120: (6T) + 5(T − 2) + 4(T − 5) all over 120 = 1⇒ (6T + 5T − 10 + 4T − 20) / 120 = 1 ⇒ (15T − 30) / 120 = 115T − 30 = 120 ⇒ 15T = 150 ⇒ T = 10 daysA’s work = T/20 = 10/20 = 1/2 of the jobA’s share = 1/2 * ₹ 5400 = ₹ 2700 Verification / Alternative check: Compute B and C: B’s work = (T − 2)/24 = 8/24 = 1/3; C’s work = (T − 5)/30 = 5/30 = 1/6. Sum = 1/2 + 1/3 + 1/6 = 1 — perfect balance. Why Other Options Are Wrong: ₹ 540, ₹ 600 are too small; ₹ 1800 understates A’s half-share. Common Pitfalls: Assuming all worked for T days; ignoring the early departures; arithmetic errors when clearing denominators. Final Answer: ₹ 2700

Work and Wages Questions