Question

Vijay had some bananas, and he divided them into two lots A and B. He sold the first lot at the rate of Rs 2 for 3 bananas and the second lot at the rate of Re 1 per banana, and got a total of Rs 400. If he had sold the first lot at the rate of Re 1 per banana, and the second lot at the rate of Rs 4 for 5 bananas, his total collection would have been Rs 460. Find the total number of bananas he had.

Answer 1

Let the number of bananas in lots A and B be x and y respectively

Case I: Cost of the first lot at the rate of ₹ 2 for 3 bananas + Cost of the second lot at the rate of ₹ 1 per banana = ₹ 400

⇒ `2/3x + y` = 400

⇒ `2x + 3y` = 1200  ......(i)

Case II: Cost of the first lot at the rate ₹ 1 per banana + Cost of the second lot at the rate of ₹ 4 for 5 bananas = Amount received

⇒ `x + 4/5y` = 460

⇒ 5x + 4y = 2300  ......(ii)

On multiplying in equation (i) by 4 and equation (ii) by 3 and then subtracting them, we get

(8x + 12y) – (15x + 12y) = 4800 – 6900

⇒ – 7x = – 2100

⇒ x = 300

Now, put the value of x in equation (i), we get

2 × 300 + 3y = 1200

⇒ 600 + 3y = 1200

⇒ 3y = 1200 – 600

⇒ 3y = 600

⇒ y = 200

∴ Total number of bananas = Number of bananas in lot A + Number of bananas in lot B

= x + y

= 300 + 200

= 500

Hence, he had 500 bananas.