Question

If the cost of bananas is increased by ₹10 per dozen, one can get 3 dozen less for ₹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)

(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.