Rahul borrowed a sum of ₹ 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 ₹ 274.95 by way of interest on borrowed sum as well as his own amountfrom the whole transaction, then what is the sum lent by him to Sachin?
(a)₹ 1200
(b)₹ 1285
(c)₹ 1690
(d)₹ 1785
(e)None of these
Answer
Answer (as printed): D
Explanation
Let the money added by Rahul be ₹ $x$. Then, $$\frac{(1150+x) \times 9 \times 3}{100}-\frac{1150 \times 6 \times 3}{100}=274.95$$ ⇔ $$1150 \times 27+27 x-1150 \times 18=27495$$ ⇔ $$27 x+1150 \times(27-18)=27495$$ ⇒ $$27 x=27495-10350=17145 \Rightarrow x=635 .$$ So, sum lent by Rahul to Sachin $=₹(1150+635)=₹ 1785$.
Explanation as extracted from the printed page; notation may be imperfect.