Multiple choice

Aastha and Shagun started a business with investments of Rs.7000 and Rs.10000. After x months, Aastha left. After two more months Vijayshri joined the business with an investment of Rs.10000. If the annual profit is shared among Vijayshri, Aastha and Shagun in the ratio 10 : 7 : 24, find the respective time periods of Vijayshri, Aastha and Shagun for which they stayed that year.

  1. 5 : 5 : 12

  2. 1 : 1 : 3

  3. 1 : 1 : 4

  4. 1 : 1 : 2

  5. None of these
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A Correct answer
Explanation

Profit sharing in partnership is proportional to investment × time. Aastha invested Rs.7000 for x months, Shagun Rs.10000 for 12 months, Vijayshri Rs.10000 for (x-2) months. Their profit ratio 10:7:24 means 10000(x-2):7000x:10000×12 = 10(x-2):7x:120 = 10:7:24. Solving gives x=5, so time periods are 3:5:12 for V:A:S, which simplifies to 5:5:12 in the options.

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