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

  • question_answer
    A sum of money placed at compound interest doubles itself in 5 yr. In how many years, it would amount to 8 times of itself at the same rate of interest?

    A) 7 yr

    B) 10 yr

    C) 15 yr

    D) 20 yr

    Correct Answer: C

    Solution :

    [c] Let principal be Rs. x and the rate be R% per annum. Then. \[x\times {{\left( 1+\frac{R}{100} \right)}^{5}}=2x\] \[\Rightarrow \]   \[{{\left( 1+\frac{R}{100} \right)}^{5}}=2\]                               …(i) Let \[x\times {{\left( 1+\frac{R}{100} \right)}^{t}}=8x\] \[\Rightarrow \]   \[{{\left( 1+\frac{R}{100} \right)}^{t}}\]             \[=8={{2}^{3}}={{\left\{ {{\left( 1+\frac{R}{100} \right)}^{5}} \right\}}^{3}}\] \[\Rightarrow \]   \[{{\left( 1+\frac{R}{100} \right)}^{t}}={{\left( 1+\frac{R}{100} \right)}^{15}}\] \[\Rightarrow \]   \[t=15\,\,yr\]


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