Question : The discount on a certain sum of money, due at the end of $2\frac{1}{4}$ years at $2\frac{2}{3}$% p.a. is Rs. 78 find the sum.
Option 1: Rs. 1,278
Option 2: Rs. 1,300
Option 3: Rs. 1,378
Option 4: Rs. 1,400
Correct Answer: Rs. 1,300
Solution :
Rate = $2\frac{2}{3}$%
Time = $2\frac{1}{4}$ years
Interest = Rs. 78
Let the Principal be $x$.
Simple Interest = $\frac{\text{Principal × Rate × Time}}{100}$
$⇒78=\frac{x×2\frac{2}{3}×2\frac{1}{4}}{100}$
$⇒78=x×\frac{8}{3}×\frac{9}{4}×\frac{1}{100}$
$\therefore x = 1300$
Hence, the correct answer is Rs. 1,300.
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