Question

If the cost of bananas is increased by Rs. 10 per dozen, one can get 3 dozen less for Rs.600. Find the original cost of one dozen of bananas.

Answer 1

Let x be the original cost of a dozen bananas.
For Rs. 600 let us one gets y dozens.
`xy =600` .................... (1)

`y=600/x`

By increasing the cost of 1 dozen of bananas by Rs. 10 we get 3 dozen less bananas

`(x +10)(y - 3)=600 ` ............................(2)

Substituting the y value in (2), we get

`(x+10)(600/x-3)=600`

`(x+10)((600-3x)/x)=600`

`(10+x)(600-3x)=600x`

`6000+570x-3x^2=600x`

`6000-30x-3x^2=0`

`3(x^2+10x-2000)=0`

`x^2+10x-2000=0`

`(x+50)(x-40)=0`

`x=-50 or 40`

Since cost of bananas cannot be negative, x = 40.

So, the original cost of one dozen of bananas is Rs.40