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

Let the number of bananas in lot 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 = Amount received

…(i)

**Case II** :

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

…(ii)

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

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

- 7x = - 2100

x = 300

Now, put the value of in Eq. (i), we get

2(300) + 3y = 1200

3y = 600

y = 200

∴ Total number of bananas = Number of bananas in lot Number of bananas in lot B = x + y

x + y = 300 + 200 = 500

Hence, he had 500 bananas.

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