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Arithmetic Ability
Time and Work

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Q.

Relation Between Efficiencies 6 boys and 8 girls finish a job in 6 days and 14 boys and 10 girls finish the same job in 4 days. In how many days working together 1 boy and 1 girl can finish the work?

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Correct choice: B

Explanation:

In this kind of questions we find the work force required to complete the work in 1 day (or given unit of time) then we equate the work force to find the relationship between the efficiencies (or work rate) between the different workers. Therefore, 6B+8G = 6 days => 6(6B+8G)= 1 day (inversely proportional) => 36B+48G =1 ( by unitary method) Again 14B+10G = 4days => 56B+40G =1 so, here it is clear that either we employ 36B and 48G to finish the work in 1 day or 56B and 40G to finish the same job in 1 day. thus , we can say => 36B+48G = 56B+40G => G= 2.5B Thus a Girl is 2.5 times as efficient as a boy. Now, since 36B+48G = 1 => 36B+48(2.5 B)=1 =>156B=1 i.e., to finish the job in 1 day 156 boys are required or the amount of work is 156 boys-days Again 1G+1B=2.5B+1B=3.5B Now, since 156 boys can finish the job in 1 day so 1 boy can finish the job in 156 days Therefore, 3.5 boys can finish the job in 1×1563.5= 47 days.
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