question_answer

A 10 hec field is reaped by 2 men, 3 women and 4 children together in 10 days. If working capabilities of a man, a woman and a child are in the ratio 5 : 4 : 2, then 16 hec field will be reaped by 6 men, 4 women and 7 children in

A) 5 days              

B) 6 days

C) 7 days              

D) 8 days

Correct Answer: D

Solution :

Ratio of their efficiencies = 5 : 4 : 2

\[\therefore \]Ratio of work \[=\frac{1}{5}:\frac{1}{4}:\frac{1}{2}=4:5:10\]

\[\Rightarrow \]               \[4M=5W=10C\]

\[\Rightarrow \] \[2M+3W+4C=5C+6C+4C=15C\]

and \[6M+4W+7C=15C+8W+7W=30C\]

\[\therefore \]      \[x=\frac{15\times 16}{30\times 10}\times 10=8\,\,\text{days}\]