Question

Divide ₹8300 among A, B and C such that 4 times A's share, 5 times B's share and 7 times C's share may all be equal.

Answer 1

Given: $$4A = 5B = 7C = k$$.

Then, $$A = \frac{k}{4}$$, $$B = \frac{k}{5}$$ and $$C = \frac{k}{7}$$. 

Ratio of their shares: $$A : B : C = \frac{1}{4} : \frac{1}{5} : \frac{1}{7}$$. 

L.C.M. of 4, 5 and 7 is 140.

$$A = \frac{1}{4} \times 140 = 35$$

$$B = \frac{1}{5} \times 140 = 28$$

$$C = \frac{1}{7} \times 140 = 20$$

Ratio = $$35 : 28 : 20$$

Sum of ratio terms = $$35 + 28 + 20 = 83$$.

Total amount = ₹ 8300.

A's share = $$₹\left(8300 \times \frac{35}{83}\right) = \text{₹ } 3500$$

B's share = $$₹\left(8300 \times \frac{28}{83}\right) = \text{₹ } 2800$$

C's share = $$₹\left(8300 \times \frac{20}{83}\right) = \text{₹ } 2000$$