Question

A sum of money was borrowed at $6\%$ per annum simple interest. At the end of first year Rs. $6800$ was paid of and the rate of interest on the balance was reduced to $5\%$ per annum. If the interest for the second year was $\frac{11}{20}$ of the interest for the first year what was the original sum borrowed?

• A. Rs. $10000$
• B. Rs. $12000$
• C. Rs. $17000$
• D. Rs. $15000$

Answer 1

The correct option is C Rs. $17000$

Let the sum be Rs. $x$.

So the Principal $=P=x$, Rate $=6\%$, Time $=T=1$ yr, S.I $=$ $I_1,$ & the amount $=A$.

$\therefore I_1=\frac{PRT}{100}=\frac{x\times 6\times 1}{100}=\frac{3x}{50}.\therefore A=x+\frac{3x}{50}=\frac{53x}{50}$

Given, Rs. $6800$ was paid.

The new principal $=P=$ $\frac{53x}{50}-6800=\frac{53x-340000}{50},$ rate $=5\%$, time $=1$ yr, S.I $=$ $I_2.$

So, $I_2=\frac{PRT}{100}=\frac{(53x-340000)\times 5\times 1}{50\times 100}.$

Given that

$I_1\times \frac{11}{20}=I_2$

$\Rightarrow \frac{3x}{50}\times \frac{11}{20}=\frac{(53x-340000)\times 5\times 1}{50\times 100}$

$\Rightarrow 33x=53x-340000$

$\Rightarrow 20x=340000$

$\Rightarrow x=$ Rs. $170000.$

So, the required amount is Rs. $170000$.

Ans- Option C.