Question 6 Sanjay, Vijay and Jay invested Rs.
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Question 6
Sanjay, Vijay and Jay invested Rs. 10,000, Rs. 12,000 and Rs. 9,000 respectively in a business. Sanjay left after five months. If after ten months, a profit of Rs. 1,950 is earned, then what is the share of Vijay?
Show answer & explanation
In partnership, profit is distributed in the ratio of capital contributions weighted by time. Sanjay's contribution is 10,000 × 5 = 50,000; Vijay's is 12,000 × 10 = 120,000; Jay's is 9,000 × 10 = 90,000. The ratio is 50,000 : 120,000 : 90,000 = 5 : 12 : 9. Vijay's share = (12 / 26) × 1,950 = Rs. 900 × 4 = Rs. 3,600.
Step-by-step Derivation:
Step 1: Calculate capital contribution weighted by time (capital × months).
- Sanjay: Rs. 10,000 × 5 months = Rs. 50,000
- Vijay: Rs. 12,000 × 10 months = Rs. 120,000
- Jay: Rs. 9,000 × 10 months = Rs. 90,000
Step 2: Find the ratio of contributions.
Ratio = 50,000 : 120,000 : 90,000
Divide by 10,000: 5 : 12 : 9
Step 3: Sum of ratio parts.
Total = 5 + 12 + 9 = 26
Step 4: Calculate Vijay's share.
Vijay's share = (12 / 26) × Rs. 1,950
= (12 × 1,950) / 26
= 23,400 / 26
= Rs. 900 × (26 / 26)
= Rs. 3,600