Practicing Success
A person divided a certain sum among his three sons in the ratio 2 : 3 : 8. If he had instead divided it in the ratio $\frac{1}{2} : \frac{1}{3} : \frac{1}{8}$, the son who got the least share would have received ₹2200 more. The sum (in ₹) was: |
5980 6556 6578 5940 |
5980 |
Here, Let the amount divided be 200x : 300x : 800x Total amount = 200x + 300x + 800x = 1300x Now, If he had instead divided it in the ratio $\frac{1}{2} : \frac{1}{3} : \frac{1}{8}$ = 12 : 8 : 3 ⇒ 1st son (least) = \(\frac{12}{23}\) × 1300x ⇒ According to the question, ⇒ The son who got the least share would have received Rs. 2200 more, ⇒ \(\frac{15600x}{23}\) - 200x = 2200 ⇒ \(\frac{11000x}{23}\) = 2200 ⇒ x = 4.6 The sum was = 1300x = 1300 × 4.6 = 5980. |