Question

If cost of bananas is increased by ₹1 per dozen one can get 2 dozen banana less for ₹840 . Find the original cost of one dozen of banana .​

Answer 1

Answer:

Step-by-step explanation:

Let the cost of banana per dozen be Rs. x.

Amount for which bananas are bought = Rs. 840

No. of dozens of bananas for Rs 840  = 840/x

New cost of banana per dozen = Rs. (x + 1)

New No. of dozens of bananas for Rs 840 = 840/x+1

According to given condition,

840/x – 840 / x + 1 = 2

∴ 840[1/x – 1/x+1] = 2

∴ 840 [x+1- x / x(x+1)] = 2

∴ 840 [1/ (x2 + x)] = 2

∴ 840 = 2(x2 + x)

∴ 2x2 + 2x – 840 = 0

Dividing by 2, we get

x2 + x – 420 = 0

x2 – 20x + 21x – 420 = 0

∴  x (x – 20) + 21 (x – 20) = 0

∴  x – 20 = 0 or x + 21 = 0

∴  x = 20 or x = –21

∴  The cost of bananas cannot be negative.

∴  x = 20

The original cost of one dozen banana is Rs. 20