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If 4 men and 4 boys can do a work in 6 days, and 2 men and 5 boys can do it in 8 days, how long would 12 men and 12 boys take to finish the work?
1 day
2 days
3 days
4 days
2 days
Notice the target group (12 men + 12 boys) is exactly 3 times the first group (4 men + 4 boys). Since 3├Ч4=12, we use the inverse relationship: if the group size triples, the time taken becomes one-third.
4 men and 4 boys complete work in 6 days. 2 men and 5 boys complete work in 8 days.
Work=Efficiency├ЧTime
Notice the target group (12 men + 12 boys) is exactly 3 times the first group (4 men + 4 boys). Since 3├Ч4=12, we use the inverse relationship: if the group size triples, the time taken becomes one-third.
Students often assume men and boys have equal efficiency or attempt to add 4+4 and 2+5 directly without establishing the man-to-boy efficiency ratio.
Establish the relationship
Equate the work done by both groups: 6(4M+4B)=8(2M+5B).
24M+24B=16M+40B
Find the ratio of efficiencies
Rearrange the equation to find the ratio of 1 man (M) to 1 boy (B): 8M=16B, which simplifies to 1M=2B.
BMтАЛ=816тАЛ=12тАЛ
Calculate total work
Substitute M=2B into the first group's equation to express total work in terms of boys: 6(4(2B)+4B)=6(8B+4B)=6(12B)=72B units.
Total┬аWork=72┬аunits┬аof┬аboys
Solve for the target group
Convert the target group (12 men + 12 boys) into boys: 12(2B)+12B=24B+12B=36B. Time taken = 36B72BтАЛ=2 days.
Time=36B72BтАЛ=2
B is correct because the target group of 12 men and 12 boys is equivalent to 36 boys, and total work is 72 boy-days, resulting in 2 days.
This concept of ratios is identical to finding the 'equivalent resistance' in Physics circuits or 'stoichiometric ratios' in Chemistry.
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