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  • 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 b

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.

 

Answers (1)

Solution:
Let bananas in lot A = x
Bananas in lot B = y
According to question:
\left ( \frac{x}{3} \right )\left ( 2 \right )+y\left ( 1 \right )= 400
2x + 3y = 400 × 3
2x + 3y = 1200 … (1)
x(1) + \left ( \frac{y}{5} \right )(4) = 460
5x + 4y = 460 × 5
5x + 4y = 2300 … (2)
Multiply equation (1) by 5 and eq. (2) by 2
10x + 15y = 6000                    
10x + 8y = 4600
–         –         –
7y = 1400

y= \frac{1400}{7}= 200
Put y = 200 in eq. (1)
2x + 3(200) = 1200
2x + 600 = 1200
2x = 600
x = 300

Total number of bananas = x + y = 300 + 200 = 500

 

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