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SSC Quantitative Aptitude Simple Interest Question Bank Simple and Compound Interest (II)

  • question_answer
    A money lender borrows money at 4% per annum and pays 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. Thus, he gains Rs. 104.50 a year. The amount of money he borrows, is

    A) Rs. 4500

    B) Rs. 5000

    C) Rs. 5500

    D) Rs. 6000

    Correct Answer: B

    Solution :

    [b] Let the money borrowed be Rs. x. Interest paid by the money lender             \[=\text{Rs}.\left( x\times \frac{4}{100}\times 1 \right)=\text{Rs}.\frac{x}{25}\] Interest received by the money lender \[=\text{Rs}.\,\left[ x\times {{\left( 1+\frac{3}{100} \right)}^{2}}-x \right]\] \[=\text{Rs}.\left( x\times \frac{103}{100}\times \frac{103}{100}-x \right)=\text{Rs}.\frac{609x}{10000}\] Gain \[=\text{Rs}.\,\left( \frac{609x}{10000}-\frac{x}{25} \right)\]             \[=\text{Rs}.\,\frac{209x}{10000}\] \[\therefore \]      \[\frac{209}{10000}x=104.50\] \[\Rightarrow \]   \[209x=104.50\times 10000\] \[\Rightarrow \]   209x = 1045000 \[\Rightarrow \]   \[x=\frac{1045000}{209}=\text{Rs}\text{.}\,\,5000.\] Thus, he borrows Rs. 5000.


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