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:
Answer & explanation
Correct answer: option 1
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.