50 villages had taken 18 days to dig a pond . Calculate by using theory of variation how many extra persons will be required to dig the pond in 15 days.

Explanation

Let the number of persons =M and the number of days =D .
`because` If the number of persons increases, the number of days will decrease.
`therefore` M varies inversely as D .
`therefore M proprArr =k . 1/D[where k ne0=v.c]`
`rArr M=k/D........(1)`
As per question , if M =50 , then D=18.
`therefore` from (1) we get , 50 =`(k) /(18)rArr =900`.
`therefore M =(900)/(D) ........(2) ["from" (1)]`
Now ,putting D =15 we get , M =`(900)/(15)=60. `
The extra persons =60-50 =10.
Hence the required number of extra persons = 10.