Multiple choice

Given below are two statements based on the following: K started a business with Rs. 50,000. After a few months, L joined him with Rs. 30,000. At the end of the year, the total profit was divided between them in the ratio of 2 : 1. Statement I: L joined the business after 2 months. Statement II: The share of the profit would have been 10 : 3, if L had joined after 6 months. In the light of the above statements, choose the correct answer from the options given below:

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement I is true, but Statement II is false.

  4. Statement I is false, but Statement II is true.

  5. NA
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

K: 50k for 12 months. L: 30k for x months. Profit ratio = (50*12) / (30*x) = 600 / 30x = 20/x. Given ratio 2:1, so 20/x = 2/1 => x = 10. L joined after 12-10 = 2 months. Statement I is true. If L joined after 6 months, x = 6. Ratio = 600 / (30*6) = 600/180 = 10/3. Statement II is true.

AI explanation

Using the partnership formula, the ratio of profits is the product of investment and time, so 50000 times 12 divided by 30000 times T equals 2 divided by 1. Solving this gives T equals 10, which means L joined after 2 months, proving Statement I is true. If L had joined after 6 months, the profit ratio would be 50000 times 12 divided by 30000 times 6, which simplifies to 10 divided by 3, proving Statement II is also true. Therefore, both Statement I and Statement II are true.

Keep practicing — related questions