A money lender borrows money at 4% per annum and pays the interest at the end of the year. He lends it at 6% per annum compound interest compounded half yearly and receives the interest at the end of the year. In this way, he gains Rs. 104.50, a year. The amount of money be borrows, is ?
A. Rs. 4500
B. Rs. 5000
C. Rs. 5500
D. Rs. 6000
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let the sum Rs}}{\text{. }}x{\text{ }} \cr & {\text{Then,}} \cr & {\text{C}}{\text{.I}}{\text{. when compounded half yearly}} \cr & {\text{ = Rs}}{\text{.}}\left[ {x \times {{\left( {1 + \frac{3}{{100}}} \right)}^2} - x} \right] \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{10609}}{{10000}}x - x} \right) \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{609x}}{{10000}}} \right) \cr & {\text{C}}{\text{.I}}{\text{. when compounded yearly}} \cr & {\text{ = Rs}}{\text{.}}\left[ {x \times \left( {1 + \frac{4}{{100}}} \right) - x} \right] \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{26x}}{{25}} - x} \right) \cr & = {\text{Rs}}{\text{.}}\frac{x}{{25}} \cr & \therefore \frac{{609x}}{{10000}} - \frac{x}{{25}} = 104.50 \cr & \Rightarrow \frac{{209x}}{{10000}} = 104.50 \cr & \Rightarrow x = \left( {\frac{{104.50 \times 10000}}{{209}}} \right) \cr & \Rightarrow x = 5000 \cr} $$Related Questions on Compound Interest
A. Rs. 120
B. Rs. 121
C. Rs. 122
D. Rs. 123
E. None of these
A. 625
B. 630
C. 640
D. 650
E. None of these
A. Rs. 2160
B. Rs. 3120
C. Rs. 3972
D. Rs. 6240
E. None of these
A. Rs. 2.04
B. Rs. 3.06
C. Rs. 4.80
D. Rs. 8.30
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