# Discussion of Question with ID = 017 under Simple-Interest

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### 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 r1, t1, r2, t2 and r3, t3 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 r1 = r2 = r3 = 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.