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Question:

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

Ruhi invested a certain amount of money in two schemes

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