Multiple choice

Passage

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question.

Three friends Geet, Sumit and Kavit start a business each investing Rs. 20,000. After five months Geet withdraws Rs. 6000, Sumit withdraws Rs. 5,000 and Kavit invests Rs. 8,000 more. The profit share of Sumit is how much less than the profit share of Kavit after a year's investment? (1) The profit share of Kavit is Rs. 12,054 more than the profit share of Geet. (2) The profit share of Geet is Rs. 24,354

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statement (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Both statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The profit ratio depends on the product of investment and time. Since all initial investments and changes are known, the ratio of their profit shares is fixed. Statement (1) provides the absolute difference in profit, which allows calculating the actual shares. Statement (2) provides the absolute profit of one person, which also allows calculating the actual shares. Thus, each statement is sufficient.

AI explanation

Since the ratio of profit shares equals the ratio of the equivalent capital invested, calculate the effective investments for the year. Geet's equivalent capital is (20000 x 5) + 14000 x 7 = 198000, Sumit's is (20000 x 5) + 15000 x 7 = 205000, and Kavit's is (20000 x 5) + 28000 x 7 = 296000, giving a profit ratio of 198:205:296. Statement (1) provides the exact total profit scale factor because the difference between Kavit's and Geet's share is (296 - 198) = 98 units, which equals Rs. 12054, making one unit equal to Rs. 123, which can be multiplied by 91 to find the difference between Kavit and Sumit. Statement (2) gives Geet's share directly as Rs. 24354, which means one unit is 24354 divided by 198, and multiplying this unit value by 91 yields the required difference. Therefore, each statement independently gives the exact total profit scale needed.

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