Anuj and Rajesh each lent the same amount of money for 2 years at 8 % simple interest and compound interest, respectively. Rajesh received Rs. 64 more than Anuj. Find the money lent by each and the interest received.

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Rs. 1600 and Rs. 1664

Rs. 1609 and Rs. 1668

Rs. 1601 and Rs. 1663

Rs. 1605 and Rs. 1666

answer is A.

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Detailed Solution

For Anuj:
We have been given that Anuj has lent the money for 2 years at 8 % simple interest. So, we have,
Principal amount = P
Rate = R = 8 %
Time = T = 2 years
Now, we know that simple interest is given by :

, where S.I is the simple interest.

For Rajesh :
We have been given that Rajesh has lent the money for 2 years at 8 % compound interest. So, we have,
Principal amount = P
Rate = r = 8 % = 8100
Time = t = 2 years
Now, we know that compound interest is given by :
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So, the difference of their interests must be 64.
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Using the identity a2−b2=(a+b)(a−b)
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Now, substituting P = 10000 in equation (i), we get,
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Since, compound interest is Rs. 64 more than simple interest, therefore, we have,

Hence, the interest received by Anuj and Rajesh are Rs. 1600 and Rs. 1664 respectively.
So, option 1 is correct.

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