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Rahul borrowed a sum of Rs. 1150 from Amit at the simple interest rate of 6 p.c.p.a. for 3 Years. He then added some more money to the borrowed sum and lent it to Sachin for the same time at 9 p.c.p.a simple interest. If Rahul gains Rs. 274.95 by way of interest on borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Sachin ?

Rahul borrowed a sum of Rs. 1150 from Amit at the simple interest rate of 6 p.c.p.a. for 3 Years. He then added some more money to the borrowed sum and lent it to Sachin for the same time at 9 p.c.p.a simple interest. If Rahul gains Rs. 274.95 by way of interest on borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Sachin ? Correct Answer Rs. 1785

Let the money added by Rahul be Rs. x
Then,
$$ \Rightarrow \frac{{\left( {1150 + x} \right) \times 9 \times 3}}{{100}} - $$     $$\frac{{1150 \times 6 \times 3}}{{100}} = $$    $$274.95$$
⇒ 1150 × 27 + 27x - 1150 × 18 = 27495
⇒ 27x + 1150 × (27 - 18) = 27495
⇒ 27x = 27495 - 10350
⇒ 27x = 17145
⇒ x = 635
So, sum lent by Rahul to Sachin
= Rs. ( 1150 + 635 )
= Rs. 1785

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