Mr. Raj divides Rs. 1573 such that 4 times the 1st share, thrice the 2nd share…

Concept

When several shares are linked by a common equal value — here 4 times the first share equals 3 times the second equals 2 times the third — call that common value k. Each share is then k divided by its own multiplier, so the first, second and third shares are k/4, k/3 and k/2. Because all three are written in terms of one unknown k, the total amount gives a single equation to solve.

Applying it to this problem

1. Let the equal value be k, so 4(first) = 3(second) = 2(third) = k.

2. Then first = k/4, second = k/3 and third = k/2.

3. Their sum is the total: k/4 + k/3 + k/2 = 1573.

4. Take LCM 12: (3k + 4k + 6k)/12 = 1573, i.e. 13k/12 = 1573.

5. So k = 1573 x 12 / 13 = 18876 / 13 = 1452.

6. The second share is k/3 = 1452 / 3 = 484.

Cross-check

With k = 1452 the shares are first = 1452/4 = 363, second = 1452/3 = 484, third = 1452/2 = 726. Their sum is 363 + 484 + 726 = 1573, the original amount, and 4 x 363 = 3 x 484 = 2 x 726 = 1452, so all three weighted shares are equal. The second share is Rs. 484.