### Question

A sum of Rs. 24160 is divided into three parts such that simple interest on these parts at 10% p.a. after 11, 18 and 14 years, respectively, is same. What is the amount of the smallest part?

**A**

Rs. 6160.

**B**

Rs. 6260.

**C**

Rs. 6060.

**D**

Rs. 6360.

**Soln.**

**Ans: a**

We should use the shortcut technique here. If r_{1}, t_{1}, r_{2}, t_{2} and r_{3}, t_{3} be the rates and times for three parts with same interest amount, then the three parts must be in the ratio $1/{r_1 t_1} : 1/{r_2 t_2} : 1/{r_3 t_3}$. In our case r_{1} = r_{2} = r_{3} = 10, which cancels, so the ratio is $1/t_1 : 1/t_2 : 1/t_3$. The product of denominators is 11 × 18 × 14 = 2772. Thus, the three parts are in the ratio $252 : 154 : 198$. The parts are: 24160 × $198/{252 + 154 + 198}$, 24160 × $154/{252 + 154 + 198}$ and 24160 × $252/{252 + 154 + 198}$, which are 10080, 6160 and 7920. The smaller is Rs. 6160.