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?

Explanation:-

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