rahul-had-some-bananas-and-he-divided-them-into-two-lots

Q:) Rahul 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.

Solution: Let Rahul have bananas in first lots = x

And Let number of bananas in second lots = y

First condition

Amount of money for lot A = $\frac{2}{3}x$

Amount of money for lot B = 1.y

$\frac{2}{3}x + 1.y = 400$

Multiply by 3 in equation

⇒ 2x + 3y = 1200 —— (i)

Secon condition

Amount of money for lot A = 1.x

Amount of money for lot B = $\frac{4}{5}y$

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

Multiply by 5 in equation

5x + 4y = 2300 —–(ii)

Multiply by 5 in (i) and 2 in (ii) and substracting (i) to (ii)

5(2x + 3y) – 2(5x + 4y) = 1200 – 2300

⇒ 10x + 15 y – 10x – 20y = -1100

⇒ – 5y = -1100

⇒ y = 220

Putting the value of x in (i)

2x + 3×220 = 1200

⇒ 2x = 1200 – 660

⇒ 2x = 540

⇒ x = 540/2 = 270

Number of bananas in lot A = 270

Number of bananas in lot B = 220

https://gmath.in/ruhi-invested-a-certain-amount-of-money-in-two-schemes/