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Explanation
A, B and C start a business each investing Rs. 20000, but after 5 months;
- A withdraw Rs. 5000.
- B withdraw Rs. 4000.
- And C invests Rs. 6000 more.
Our aim is the to find out A, B and C’s total investment for 12 months so let’s get started.
- A, B and C’s total investment for first 5 months (A = 20000 x 5 = 100000, B = 20000 x 5 = 100000 and C = 20000 x 5 = 100000).
- As, the profit is needed to be calculated for the 12 months so remaining time of investment will be 7 months.
- In the next step; retracted amount will be subtracted from the actual investment which is 20000 (A = 20000 – 5000 = 15000, B = 20000 – 4000 = 16000, C = 20000 + 6000 = 26000 because A withdraws 5000, B withdraws 4000 and C invests 6000 more).
- Now, to calculate A, B and C’s total investment for next 7 months (A = 15000 x 7 = 105000, B = 16000 x 7 = 112000 and C = 26000 x 7 = 182000).
- Finally; A, B and C’s total investment for 12 months (A = 100000 + 105000 = 205000, B = 100000 + 112000 = 212000, C= 100000 + 182000 = 282000)
Now;
- A’s share in profit = (A’s ratio of investment x total profit) / total ratio
- B’s share in profit = (B’s ratio of investment x total profit) / total ratio
- C’s share in profit = (C’s ratio of investment x total profit) / total ratio
To Find
A, B and C’s share in annual profit = ?
Solution
A, B and C’s total investment for 5 months
A = 20000 x 5 = 100000
B = 20000 x 5 = 100000
C = 20000 x 5 = 100000
After 5 months; A retracts 5000, B retracts 4000 and C invests 6000 more;
A = 20000- – 5000 = 15000
B = 20000 – 4000 = 16000
C = 20000 + 6000 = 26000
Now; A, B and C’s total investment for 7 months
A = 15000 x 7 = 105000
B = 16000 x 7 = 112000
C = 26000 x 7 = 182000
Finally; A, B and C’s total investment for 12 months
A = 100000 + 105000 = 205000
B = 100000 + 112000 = 212000
C = 100000 + 182000 = 282000
Profit ratio is equal to investment ratio. So,
A : B : C = 205000 : 212000 : 282000
A : B : C = 205 : 212 : 282 (and A + B + C = 699)
A’s share in profit = (205 x 69900)/699 = 20500
B’s share in profit = (212 x 69900)/699 = 21200
C’s share in profit = (282 x 69900)/699 = 28200
So, share of A, B and C in profit is Rs. 20500, Rs.21200 and Rs. 28200 respectively, which is our required answer.
Conclusion
A, B and C start a business each investing Rs. 20000. After 5 months A withdraws Rs. 5000 , B withdraws Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69900 was recorded. The share of A, B and C will be Rs. 20500, Rs. 21200 and Rs. 28200 respectively.
