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If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 40 men and 20 boys in doing the same type of work will be:
4 days
5 days
2 days
3 days
2 days
Use the ratio of work capacity: (6M + 8B) * 10 = (26M + 48B) * 2 simplifies to 60M + 80B = 52M + 96B, resulting in 8M = 16B or 1M = 2B. Convert all to boys: (62 + 8) boys * 10 = 200 unit work. Required group: (402 + 20) boys = 100 boys. Time = 200/100 = 2 days.
6 men and 8 boys can complete a work in 10 days. 26 men and 48 boys can complete the same work in 2 days.
(M1тАЛD1тАЛ)=(M2тАЛD2тАЛ)
Use the ratio of work capacity: (6M + 8B) * 10 = (26M + 48B) * 2 simplifies to 60M + 80B = 52M + 96B, resulting in 8M = 16B or 1M = 2B. Convert all to boys: (62 + 8) boys * 10 = 200 unit work. Required group: (402 + 20) boys = 100 boys. Time = 200/100 = 2 days.
Confusing 'man-days' with the actual number of workers; always convert men into boy-equivalents first.
Establish the relationship between Men and Boys
Since the work is the same, we equate the total man-days: 10(6M+8B)=2(26M+48B). Dividing by 2 gives 5(6M+8B)=26M+48B.
30M+40B=26M+48BтЗТ4M=8BтЗТ1M=2B
Calculate total work in terms of 'Boy-Days'
Substitute 1M=2B into the first group's capacity: 6(2B)+8B=12B+8B=20B. The total work is 20B├Ч10=200 boy-days.
Total┬аWork=200┬аboy-days
Find the time for the target group
The target group is 40 men and 20 boys. In boy units: 40(2B)+20B=80B+20B=100B. Time = Total Work / Capacity of target group.
Time=100B200BтАЛ=2┬аdays
C is correct because the calculated time for 40 men and 20 boys is 2 days.
This type of equivalence problem is common in Pipes and Cisterns; always try to convert all variables to the smaller unit first.
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