Ten boys or twenty girls can complete a job in 10 days. In how many days can a boy and a girl complete it

Options

A. 50
B. `58(1)/(3)`
C. `66(2)/(3)`
D. 70

Answer

C

Explanation

Method 1:
10 boys can complete `(1)/(10)`th of the job in 1 day.
`:.` Each boy can complete `(1)/(10)=(1)/(100)`th of the job in a day.
Similarly each girl can complete `(1)/(100)+(1)/(200)=(3)/(200)`th of the job in 1 day.
`:.` They can complete the job in `(200)/(3)` days`=66^(2//3)` days.
Method 2:
10 boys are as efficient as 20 girls.
`:.` Each boy is as efficient as 2 girls.
`:.` A boy and a girl are as efficient as 3 girls.
Total job`=(20)(10)=100` girl days.
Required time =Time taken by 3 girls to complete it
`=(200)/(3)` days `=66(2)/(3)` days