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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 25 boys in doing the same type of work will be:
6 days
5 days
4 days
8 days
8 days
Express work as 10(6M+8B)=2(26M+48B). Simplify to find the ratio M:B, then use M1тАЛD1тАЛ=M3тАЛD3тАЛ to solve for D3тАЛ.
6 men and 8 boys do work in 10 days. 26 men and 48 boys do work in 2 days.
(M1тАЛ├ЧD1тАЛ)=(M2тАЛ├ЧD2тАЛ)
Express work as 10(6M+8B)=2(26M+48B). Simplify to find the ratio M:B, then use M1тАЛD1тАЛ=M3тАЛD3тАЛ to solve for D3тАЛ.
Confusing the number of days taken by boys with the total number of individuals, or miscalculating the ratio of man-to-boy efficiency.
Set up the work equivalence equation
Since the amount of work is the same, the product of people and days must be equal: 10(6M+8B)=2(26M+48B)
60M+80B=52M+96B
Solve for the efficiency ratio of men to boys
Rearrange the equation to isolate M and B: 60MтИТ52M=96BтИТ80B, which simplifies to 8M=16B. Thus, 1M=2B.
M=2B
Calculate total work in terms of boys
Substitute M=2B into the first scenario's work expression: Work=10(6(2B)+8B)=10(12B+8B)=10(20B)=200B-days.
Work=200B
Calculate days for 25 boys
If 25 boys perform the work, time D=25B200BтАЛ=8 days.
D=8
D is correct because the calculated time taken by 25 boys is 8 days.
This is a classic 'Man-Day' problem. Always convert the entire workforce to the lowest common unit (here, boys) to solve for time.
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