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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. Find the Share of Each?

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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.

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