Multiple choice

A, B, and C entered into a partnership by investing certain amounts for 12 months, X months, and (12 - X) months, respectively. Find the value of X. Statement I: B invested 75% more than A, and C invested twice the amount invested by B. Statement II: At the end of the partnership, the total profit earned was Rs. 900, and B received Rs. 150 as profit share. Statement III: The ratio of B's share of the profit to the total profit is 1 : 6.

  1. Statements I and II taken together are necessary to answer the question

  2. Either statement I and II together or statement I and III together sufficient to answer the question

  3. All the three statements taken together are necessary to answer the question

  4. Statements II and III together are necessary to answer the question

  5. Statements I and III together are necessary to answer the question
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Profit share ratio is proportional to (Investment * Time). Let A's investment be 'a'. B = 1.75a, C = 3.5a. Profit shares: A: 12a, B: X * 1.75a, C: (12-X) * 3.5a. Statement I gives the ratio of investments. Statement III gives B's share relative to total. Together, they allow solving for X. Statement II is redundant if III is used, but I and II also provide enough info.

AI explanation

To find the value of X, you must establish the investment ratio and the profit ratio of the partners. Statement I provides the investment ratio by showing B invested 75% more than A and C invested twice B, which allows the investments to be expressed in terms of A. Statement II gives the total profit and B's profit, allowing you to find B's profit ratio, which can be combined with Statement I to solve for X. Alternatively, Statement III directly provides B's profit ratio to the total profit, which when combined with Statement I's investment ratio, also allows you to solve for X. Therefore, either statement I and II together or statement I and III together are sufficient to answer the question.

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