A sum of ₹17,600 was divided between Jeevan, Praveen and Kanan, such that the ratio of the sums received by Jeevan and Praveen was 5 : 8, while the ratio of the sums received by Praveen and Kanan was 3 : 2. How much money did Jeevan receive as his share?

Correct option is C

Given:
The total sum of ₹17,600 is divided among Jeevan, Praveen, and Kanan in such a way that:
The ratio of the sums received by Jeevan and Praveen is 5:8.
The ratio of the sums received by Praveen and Kanan is 3:2.
Solution:
Let,
Jeevan's share = $$5x \quad \text{and} \quad \text{Praveen's share} = 8x$$​​
Praveen's share = $$3y \quad \text{and} \quad \text{Kanan's share} = 2y$$​​
8x = 3y
y = $$\frac{8x}{3}$$​​
Jeevan’s share + Praveen’s share + Kanan’s share = 17600

5x + 8x + 2y = 17600 ......(i)

Substitute $$y = \frac{8x}{3}$$​ into the equation:

5x + 8x + $$2 \times \frac{8x}{3} = 17600$$​

13x +$$\frac{16x}{3} = 17600$$​

39x + 16x = 52800

55x = 52800

x =$$\frac{52800}{55} = 960$$ 

Now, Jeevan's share is:
5x = $$5 \times 960 = 4800$$​​
Jeevan received ₹4,800.
Thus, the correct option is (c) 4,800

Alternate Method:

Jeevan’s share + Praveen’s share + Kanan’s share = 17600

Sum of Ratio = 15 + 24 + 16 = 55

Jeevan's share = $$\frac{17600}{55} \times 15 = 4800$$​​