An agricultural co- operative society of village Naraynpur has purchased a tractor . Previously 2400 bighas of land were cultivated by 25 ploughs in 36 days . Now half of the land can be cultivated only by that tractor in 30 days . Calculate by using the theory of variation , the number of ploughs work equaly with one tractor .

Explanation

Let the quantity of land G bighas .
Number of ploughs =P and time of cultivation =D days .
We know that if number of ploughs is cosntant , then the quantity of land varies directly with time of cultivation , i.e , G `prop` D when P is constant
Again if time of cultivation is cosntant , the quantity of land varies directly with number of ploughs , i.e G `prop ` P , when D is constant.
Then by theorem of joint variation , G `prop` PD (where P and D are both variation ) `rArr` G =k . PD
(where k `ne` 0= variation constant )
`therefore` G =k.PD .........(1)
As per question , if G =2400 and P =25 , then D =36
`therefore` from (1) we get , 2400 =k.`25xx36`
or , k =`(2400)/(25xx36)=(96)/(36) =8/3 `
`therefore` (1) becomes G =`8/3` PD ..........(2)
Now putting G =`(2400)/2=1200 and D =30` in (2) we get ,
1200=`8/3xxPxx30 or, P =(1200xx3)/(8xx30) =15` .
Hence the required number of ploughs work equally with one tractor is 15 .