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?

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Accepted Answer

**Solution:**

1. Let the amounts received by Jeevan, Praveen, and Kanan be *J*, *P*, and *K* respectively.

2. Given the ratio of Jeevan to Praveen is:
   $$J : P = 5 : 8$$

3. Given the ratio of Praveen to Kanan is:
   $$P : K = 3 : 2$$

4. To combine these ratios, express *P* in terms of a common variable:
   - From the first ratio, *J = 5x* and *P = 8x*.
   - From the second ratio, *P = 3y* and *K = 2y*.

5. Since *P* is common, equate the two expressions for *P*:
   $$8x = 3y \ ightarrow y = \frac{8x}{3}$$

6. Now express *K* in terms of *x*:
   $$K = 2y = 2 	imes \frac{8x}{3} = \frac{16x}{3}$$

7. Sum of all shares is ₹17,600:
   $$J + P + K = 17600$$
   Substitute values:
   $$5x + 8x + \frac{16x}{3} = 17600$$

8. Combine terms:
   $$13x + \frac{16x}{3} = 17600$$
   Multiply both sides by 3 to clear denominator:
   $$3 	imes 13x + 16x = 3 	imes 17600$$
   $$39x + 16x = 52800$$
   $$55x = 52800$$

9. Solve for *x*:
   $$x = \frac{52800}{55} = 960$$

10. Calculate Jeevan's share:
    $$J = 5x = 5 	imes 960 = 4800$$

**Answer:** ₹4,800

**Note:** The closest option to ₹4,800 is option (d) ₹4,800. However, the provided options have ₹4,750 as correct. Rechecking the calculation:

- Step 6: *K = \frac{16x}{3}* is correct.
- Step 7: Sum = *5x + 8x + \frac{16x}{3} = 17600*.
- Combine terms:
  $$5x + 8x = 13x$$
  So,
  $$13x + \frac{16x}{3} = 17600$$
  Multiply both sides by 3:
  $$39x + 16x = 52800$$
  $$55x = 52800$$
  $$x = 960$$

- Jeevan's share:
  $$5x = 5 	imes 960 = 4800$$

Therefore, the correct answer is ₹4,800 (option d).

**Answer:** ₹4,800

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