Mathematics

The odd one out is option C (VWYZ) because it does not consist of four consecutive letters in the alphabet, unlike the other options. Options A (KMNL), B (PRSQ), and D (JLMK) each contain four consecutive letters rearranged in a similar pattern. Specifically, KMNL is a rearrangement of K, L, M, N; PRSQ is a rearrangement of P, Q, R, S; and JLMK is a rearrangement of J, K, L, M. However, VWYZ skips the letter X and thus breaks the pattern of consecutive letters. Therefore, VWYZ is the odd one out.

Options A (343), C (1331), and D (2197) are all perfect cubes (7³, 11³, and 13³ respectively), while option B (121) is a perfect square (11²). Therefore, B does not belong to the group of perfect cubes.

Option B (28) is the only number that is not a perfect square. 16 (4²), 36 (6²), and 64 (8²) are perfect squares, while 28 is not.

A's initial investment is Rs.300 and B's is Rs.400. After the first year, A's share of profit is (300/(300+400)) * 210 = Rs.90, which he reinvests, making his new investment 300 + 90 = Rs.390. B does not reinvest, so his investment remains Rs.400. The ratio of their investments for the second year is 390:400, which simplifies to 39:40. Therefore, the second year's profit should be divided in the ratio 39:40.

A receives 10% of the total profit as a managing partner, which is Rs.960 (10% of Rs.9,600). The remaining profit is Rs.8,640 (Rs.9,600 - Rs.960), which is divided in the ratio of their capitals (A:B = 15,000:25,000 = 3:5). A's share of this remaining profit is (3/8) × 8,640 = Rs.3,240. Therefore, total money received by A = Rs.960 + Rs.3,240 = Rs.4,200. Hence, option D (Rs.4,200) is correct.

In a partnership where partners invest different amounts for different periods, the profit is shared in proportion to the product of the capital invested and the time for which it is invested. For example, if Partner A invests Rs. 10,000 for 12 months and Partner B invests Rs. 15,000 for 6 months, their profit shares are proportional to 10,000×12 = 120,000 and 15,000×6 = 90,000 respectively. The total units are 210,000. If the total profit is Rs. 21,000, Partner A's share is (120,000/210,000)×21,000 = Rs. 12,000 and Partner B's share is (90,000/210,000)×21,000 = Rs. 9,000. This confirms that profit sharing is proportional to capital invested multiplied by the time invested.

Option B (4) is the only even number in the group, while the others (3, 5, 9) are odd numbers. Therefore, 4 does not belong to the group of odd numbers.

The letters A, E, and I are vowels, while R is a consonant. Therefore, R does not belong to the group of vowels.

Both 30 and 630 are divisible by 3 and 5. 10 and 520 are divisible by 5 but not by 3. Therefore, the number that does not belong to the group based on divisibility by both 3 and 5 is 10 (option C).

First, calculate the working partner A's share: 5% of Rs.7400 = Rs.370. Remaining profit = Rs.7400 - Rs.370 = Rs.7030. Calculate each partner's capital-time product: A = 6500*6=39000, B=8400*5=42000, C=10000*3=30000. Total = 39000+42000+30000=111000. C's share = (30000/111000)*7030 ≈ Rs.1900. Therefore, the correct share of C in the total profit is approximately Rs.1900, which corresponds to option B.