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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.
Solution
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
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