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

  • question_answer
    A man borrowed some money and agreed to pay-off by paying Rs. 3150 at the end of the 1st year and Rs. 4410 at the end of the 2nd year. If the rate of compound interest is 5% per annum, then the sum is [SSC CGL Tier II, 2017]

    A) Rs. 5000

    B) Rs. 6500

    C) Rs. 7000

    D) Rs. 9200

    Correct Answer: C

    Solution :

    [c] \[r=5%,\]\[{{A}_{1}}=\text{Rs}.\,\,3150,\] \[{{A}_{2}}=\text{Rs}.\,4410\] Now,     \[{{A}_{1}}={{P}_{1}}{{\left( 1+\frac{r}{100} \right)}^{t}}\] \[\Rightarrow \]   \[3150={{P}_{1}}{{\left( 1+\frac{5}{100} \right)}^{1}}\] \[\Rightarrow \]   \[3150={{P}_{1}}\times \frac{21}{20}\] \[\Rightarrow \]   \[{{P}_{1}}=\frac{3150\times 20}{21}\]\[\Rightarrow \]\[{{P}_{1}}=\text{Rs}.\,\,3000\] Now,     \[{{A}_{2}}={{P}_{2}}{{\left( 1+\frac{r}{100} \right)}^{t}}\] \[\Rightarrow \]   \[4410={{P}_{2}}{{\left( 1+\frac{5}{10} \right)}^{2}}\] \[\Rightarrow \]   \[4410={{P}_{2}}\times {{\left( \frac{21}{20} \right)}^{2}}\] \[\Rightarrow \]   \[{{P}_{2}}=\frac{4410\times 400}{441}\]\[\Rightarrow {{P}_{2}}=\text{Rs}\text{.}\,\,4000\] \[\therefore \]      Total sum \[={{P}_{1}}+{{P}_{2}}\] \[=3000+4000=\text{Rs}\text{.}\,\,7000\]


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