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

Given:

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

To do:

We have to find the total number of bananas he had.

Solution:

Let the number of bananas in lot A and the number of bananas in lot B be $x$ and $y$ respectively.

The total number of bananas $=x+y$.

According to the question,

$x\times\frac{2}{3} + y\times1 = 400$

$3(\frac{2x}{3}+y)=3(400)$        (Multiplying both sides by 3)

$2x+3y=1200$.....(i)

$x\times 1 + y\times \frac{4}{5} = 460$

$5(x+\frac{4y}{5})=5(460)$      (Multiplying both sides by 5)

$5x+4y=2300$.....(ii)

Adding equations (i) and (ii), we get,

$2x+3y+5x+4y=1200+2300$

$7x+7y=3500$

$7(x+y)=7(500)$

$x+y=500$ 