Question

The price of banana is Rs 30 a dozen .Aditya can buy 12 dozen banana with the amount he has .if the price of banana is increased by Rs 10 per dozen, how many dozen banana can he buy ?

Answer 1

Let x be the original cost of a dozen bananas. For Rs.600 let us one gets y dozens.

xy = 600 … (1)

(x+10)(y-3) = 600 … (2)

From (1) y = 600/x. Putting that value in (2), we get,

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

(x+10)(600–3x)/x = 600 or

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

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

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

2000 - 10x - x^2 = 0

x^2 + 10x - 2000 = 0

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

So x = -50 or 40. Since cost of bananas cannot a negative figure, x = 40.

So at Rs.40 per dozen one can buy 15 dozens for Rs.600. If the cost goes up by Rs.10, the person can get 600/(40+10) = 600/50 = 12 dozens which is 3 dozens short of the previous purchasing power!

So the original cost of bananas is Rs.40 per dozen.