Question : A sum of money invested at a certain rate of simple interest per annum amounts to INR 14,522 in seven years and to INR 18,906 in eleven years. Find the sum invested (in INR).
Option 1: 6,850
Option 2: 6,900
Option 3: 6,800
Option 4: 6,750
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Correct Answer: 6,850
Solution :
Amount of sum of money invested for 7 years = INR 14,522
Amount of sum of money invested for 11 years = INR 18,906
⇒ 4 year's simple interest = 18906 – 14522 = INR 4,384
⇒ 1 years's simple interest = $\frac{4384}{4}$ = INR 1,096
⇒ 7 year's simple interest = 1096 × 7 = INR 7672
$\therefore$ The sum invested = 14522 – 7672 = INR 6,850
Hence the correct answer is 6,850.
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