A sum of Rs 18750 is left by will by a father to be divided between tw

1.	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» (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.

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»

(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.