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Question 13
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 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 for 5 bananas, his total collection would have been Rs. 460. Find the total number of bananas he had.

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Solution

Let the number of bananas in lots A and B be x and y respectively
Case I: Cost of the first lot at the rate of Rs. 2 for 3 bananas + Cost of the second lot at the rate

Of Rs.1 per banana = amount received
23x+y=400
2x+3y=1200 ...(i)
Case II: Cost of the first lot at the rate of Rs.1 per banana and the second lot at the rate of Rs. 4 for 5 bananas = amount received
x+45y=460
5x+4y=2300 ...(ii)

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

8x + 12y = 4800

15x + 12y = 6900

-7x = - 2100

x = 300

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

2 × 300 + 3y = 1200

600 + 3y = 1200

3y = 1200 – 600

3y = 600

y = 200

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

= 300 + 200 = 500

Hence, he had 500 bananas.


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