Question

A sum of Rs 18750 is left by will by a father to be divided between two sons, 12 and 14 years of age, so that when they attain maturity at 18, the amount received by each of them at 5 per cent simple interest will be the same. Find the sum allotted at present to each son ? 

(a) Rs 9500, Rs 9250 

(b) Rs 8000, Rs 1750 

(c) Rs 9000, Rs 9750 

(d) Rs 10000, Rs 8750

Answer 1

(c) Rs 9000, Rs 9750

Let sum left for the 12 years old and 14 years old sons be Rs x and Rs (18750 – x) respectively. Then,

\(\frac{x\times6\times5}{100} + x = \frac{(18750-x)\times4\times5}{100} + (18750-x)\)

⇒ \(\frac{30x}{100} +x =3750-\frac{20x}{100}+18750-x\)

⇒ \(\frac{50x}{100} +2x =22500⇒\frac{250x}{100}= 22500\)

⇒ x = Rs \(\frac{22500\times100}{250}\) = Rs 9000

∴ The sum allotted to the other son is Rs 9750.