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If a certain amount of at a certain rate (p.a.) compounded annually becomes Rs 50400 in 3 years and Rs 241920 in 6 years then find the certain amount of sum ?1. Rs 80002. Rs 100003. Rs 125004. Rs 105005. None of these |
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Answer» Correct Answer - Option 4 : Rs 10500 Given: Amount after 3 years is Rs 50400. Amount after 6 years is Rs 241920. Formula Used: Amount = \(P × {\left( {1 + \frac{R}{{100}}} \right)^n}\) CI = Amount - Principal = \(P × {\left( {1 + \frac{R}{{100}}} \right)^n}\) - P = \(P × \left\{ {{{\left( {1 + \frac{R}{{100}}} \right)}^n} - 1} \right\}\) Calculation: Let the sum be Rs x. The rate of interest be R%. According to the question, Amount for 3 years = 50400 ⇒ \(x × {\left( {1 + \frac{R}{{100}}} \right)^3}\) = 50400 ....(I) Amount for 6 years = 241920 ⇒ \(x × {\left( {1 + \frac{R}{{100}}} \right)^6}\) = 241920 ....(II) On dividing (II) ÷ (I) ⇒ \({\left( {1 + \frac{R}{{100}}} \right)^3}\) = 241920/50400 ⇒ \({\left( {1 + \frac{R}{{100}}} \right)^3}\) = 4.8 ....(III) On putting the value of equation (III) in(I) ⇒ x × 4.8 = 50400 ⇒ x = 10500 Therefore, the certain amount of sum is Rs 10500. |
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