Question

Shruti lent some money to Pallavi at $5$% p.a. simple interest. Pallavi lent the whole amount to Niki on the same day at $8\frac{1}{2}$% p.a. In this transaction after a year, Pallavi earned a profit of Rs. $350$. Find the sum of money lent by Shruti to Pallavi.

• A. Rs. $9000$
• B. Rs. $11000$
• C. Rs. $10000$
• D. Rs. $8000$

Answer 1

The correct option is C Rs. $10000$

Let $x$ be the amount Shruti lends to Pallavi.

Interest ${SI}_1$ to be paid bt Pallavi after $1$ year is $\frac{PRT}{100}$

where, $P=x,R=5$% $\left(given\right),T=1$

${SI}_1=\frac{(x\times 5\times 1)}{100}=\frac{x}{20}$

Now, Pallavi lent the same amount to Niki at $8.5$% rate for the same period $1$ year.

Interest ${SI}_2$ to be paid by Niki will be given by

${SI}_2=\frac{(x\times 8.5\times 1)}{100}=\frac{17x}{200}$

Given that Pallavi earned a profit of $Rs.350$

$\Rightarrow {SI}_2-{SI}_1=350\Rightarrow \frac{7x}{200}=350\Rightarrow x=10000$

$\therefore$ Shruti lent $Rs.10000$ to Pallavi.