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Question
Anuj had some chocolates, and he divided them into two lots A and B. He sold the first lot at the rate of ₹ 2 for 3 chocolates and the second lot at the rate of ₹ 1 per chocolate, and got a total of ₹ 400. If he had sold the first lot at the rate of ₹ 1 per chocolate, and the second lot at the rate of ₹4 for 5 chocolates, his total collection would have been ₹460. Find the total number of chocolates he had.
Solution
Let the number of chocolates in lot A be x
And let the number of chocolates in lot B be y
∴ Total number of chocolates = x + y
Price of 1 chocolate = ₹ `2/3`, so for x chocolates = `2/3`x and price of y chocolates at the rate of ₹ 1 per chocolate = y.
∴ By the given condition `2/3`x + y = 400
⇒ 2x + 3y = 1200 ......(i)
Similarly x + `4/5`y = 460
⇒ 5x + 4y = 2300 ......(ii)
By solving (i) and (ii) we get
x = 300 and y = 200
∴ x + y = 300 + 200 = 500
So, Anuj had 500 chocolates.
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