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B borrows money from A at 6% p.a. simple interest, for the first year, and lends it to C at compound interest of 10% p.a, for the second year. If B collects the money back from C after the completion of the second year, then what is the percentage profit for B in the overall transaction?
1. 10%
2. 5%
3. 4%
4. 8%

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Correct Answer - Option 1 : 10%

Formulae Used:

Simple Interest (SI), on a Principal P for a time period of T years, at a rate of R% per annum, is:

SI = (P × R × T)/100

Amount received at Simple Interest = P + SI

Amount received on a principal at a rate of R% per annum for a time period of T, when compounded annually:

Amount = P × [1 + (R/100)]T

Calculation:

Let the money initially with A be Rs.x

So, the amount received by B after 1 year = x + [(x × 6 × 1)/100] = 1.06x

This amount becomes the principal for B

So, the amount collected with C after the second year is:

Amount = 1.06x × [1 + (10/100)]1 = 1.166x

So, when B collects this money back from C, the profit made by him is:

[(1.166x – 1.06x)/1.06x] × 100 = 10%

∴ The profit of B in the overall transaction is 10%

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