Multiple choice

P started a business with Rs. 80,000. After 2 months, Q joined him with Rs. 1,20,000. R joined them after some more time with Rs. 2,40,000. At the end of the year, out of a total profit of Rs. 7,50,000, R gets Rs. 3,00,000 as his share. How many months after Q joined the business, did R join?

  1. 5 months

  2. 6 months

  3. 4 months

  4. 3 months

  5. 8 months
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let R join x months after Q. Q joined 2 months after P. P invested for 12 months, Q for 10 months, R for (10-x) months. Profit ratio: (80000*12) : (120000*10) : (240000*(10-x)) = 96 : 120 : 24(10-x) = 4 : 5 : (10-x). R's share = 300000/750000 = 2/5. So (10-x) / (4+5+10-x) = 2/5. (10-x)/(19-x) = 2/5. 50-5x = 38-2x. 12 = 3x, x = 4.

AI explanation

Using the partnership principle that profit share is proportional to the product of investment and time, P's capital is 960000 and Q's is 1200000. R's profit of Rs. 300000 out of a total of Rs. 750000 means R's share is 2/5, so his capital multiplied by his time equals 1440000. Dividing this by R's investment of Rs. 240000 gives his time in the business as 6 months, meaning he joined 6 months after the business started; since Q joined after 2 months, R joined 4 months after Q.

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