(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.