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?

The correct answer is ₹4,800.

Step 1: Understand the given ratios.

The total sum to be divided among Jeevan, Praveen, and Kanan is ₹17,600.

The ratio of the share of Jeevan to Praveen is:

$\text{Jeevan}:\text{Praveen}=5:8$

The ratio of the share of Praveen to Kanan is:

$\text{Praveen}:\text{Kanan}=3:2$

Step 2: Combine the ratios to find a common ratio (Jeevan : Praveen : Kanan).

To write a combined ratio, the value corresponding to Praveen in both ratios must be equal. The least common multiple (LCM) of 8 and 3 is 24.

Multiply the terms of the first ratio ($5:8$) by 3:

$\text{Jeevan}:\text{Praveen}=(5\times 3):(8\times 3)=15:24$

Multiply the terms of the second ratio ($3:2$) by 8:

$\text{Praveen}:\text{Kanan}=(3\times 8):(2\times 8)=24:16$

Now that Praveen's share is represented by 24 in both ratios, the combined ratio is:

$\text{Jeevan}:\text{Praveen}:\text{Kanan}=15:24:16$

Step 3: Calculate total ratio parts.

The sum of all ratio parts is:

$\text{Total Parts}=15+24+16=55$

Step 4: Determine Jeevan's share.

Jeevan receives 15 parts out of the total 55 parts:

$\text{Jeevan's Share}=\frac{15}{55}\times \text{₹17,600}$

Simplify the fraction $\frac{15}{55}$ by dividing the numerator and denominator by 5:

$\text{Jeevan's Share}=\frac{3}{11}\times \text{₹17,600}$

Divide ₹17,600 by 11:

$\frac{\text{17,600}}{11}=\mathrm{1,600}$

Multiply by 3:

$\text{Jeevan's Share}=3\times \text{₹1,600}=\text{₹4,800}$

Hence, Jeevan received ₹4,800 as his share.