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

  • question_answer
    A man borrows money at 3% per annum interest payable yearly and lend it immediately at 5% interest (compound) payable half-yearly and thereby gains Rs. 330 at the end of the year. The sum borrowed is [SSC CGL Tier II, 2014]

    A) Rs. 17000

    B) Rs 16500

    C) Rs. 15000

    D) Rs. 160005

    Correct Answer: D

    Solution :

    [d] Let the sum borrowed be Rs. x. Then, SI on Sum \[=\frac{P\times R\times T}{100}\]      [here, R = 3, T = 1]             \[=\frac{x\times 3\times 1}{100}=\text{Rs}.\frac{3x}{100}\] CI on the sum when compound half yearly \[=\left[ P{{\left( 1+\frac{R/2}{100} \right)}^{2x}}-P \right]\]       [Here, R = 5, n = 1] \[=x\left[ {{\left( 1+\frac{5}{2\times 100} \right)}^{2}}-1 \right]\] \[=x\left[ {{\left( 1+\frac{1}{40} \right)}^{2}}-1 \right]=x\left[ {{\left( \frac{41}{40} \right)}^{2}}-1 \right]\] \[=x\left[ \frac{1681}{1600}-1 \right]=x\left[ \frac{81}{1600} \right]\]             His gain \[=CI-SI=330\] \[=\frac{81x}{1600}-\frac{3x}{100}=330\] \[=\frac{81x-48x}{1600}=330\] \[\Rightarrow \]   \[x=\frac{330\times 1600}{33}=\text{Rs}.\,\,16000\]


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