Discussion of Question with ID = 014 under Simple-Interest

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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 r1, t1, r2, t2 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 r1 = r2 = 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.