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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