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### Question

A sum of Rs. 1540 is divided into two parts such that simple interest on these parts at 10% p.a. after 2 and 9 years, respectively, is same. What is the amount of the smaller part?

**A**

Rs. 280.

**B**

Rs. 380.

**C**

Rs. 180.

**D**

Rs. 480.

**Soln.**

**Ans: a**

We should use the shortcut technique here. If r_{1}, t_{1}, r_{2}, t_{2} be the rates and times for two parts with same interest amount, then the two parts must be in the ratio $1/{r_1 t_1} : 1/{r_2 t_2}$. In our case r_{1} = r_{2} = 10, which cancels, so the ratio is $1/t_1 : 1/t_2$. Thus, the two parts are in the ratio $t_2 : t_1$. The parts are: 1540 × $9/{2 + 9}$, and 1540 × $2/{2 + 9}$, which are 1260 and 280. The smaller is Rs. 280.