If 15 farmers can cultivate 18 bighas of land in 5 days, determine by using theory of variation the number of days required by 10 farmers to cultivate 12 bighas of land .

Explanation

Let the number of farmers = F , the amount of land =G and the number of days =D , `therefore` if the number of farmers be increased the amount of caltivated land also increases , but the number of days will decreased.
`therefore ` F varies directly with G , but inversely with D .
` therefore F prop (G)/(D) rArr F =k .(G) /(D) ` [when k `ne ` 0 = variation constant ]
` therefore F =k.(G)/(D) ............(1) `
As per question , if F = 15, G =18 , then D =5.
` therefore` from (1) we get , 15 =k `(18) /(5) rArr k=(75)/(18)=(25)/(6) ` .
`therefore `(1) becomes , F =`(25)/(6).(G) /(D) ...........(2)`
Now , putting F =10 , G 12 in (2) we get , 10 =`(25)/(6) .(12)/(D) or , 10 D =50 or , D (50)/(10) =5`
Hence the required number of days =5 .