Mathematics

To find A's share of the rent, we calculate the total feed consumption for A and B based on the given equivalences. Using the ratios, we convert horses and cows into sheep equivalents, sum the total feed-months for both A and B, and then find A's proportion of the total. This results in A paying 2/3 of the rent.

To determine which number does not belong to the group based on divisibility by 3, we check the sum of the digits of each number. A number is divisible by 3 if the sum of its digits is divisible by 3. - 35: 3 + 5 = 8 (not divisible by 3) - 48: 4 + 8 = 12 (divisible by 3) - 75: 7 + 5 = 12 (divisible by 3) - 84: 8 + 4 = 12 (divisible by 3) Therefore, 35 is not divisible by 3, while the others are. Hence, 35 does not belong to the group.

A invests Rs.50,000 total capital, B's share is Rs.25,000 and pays A 10% interest = Rs.2,500. A receives Rs.1,500 per month = Rs.18,000 annually as working partner. Let total profit be P. After paying interest, remaining profit = P - 2,500. A's share of remaining profit = (P - 2,500 - 18,000)/2 + 18,000 + 2,500. B's share = (P - 2,500)/2. Given A's income is twice B's: A = 2B. Solving gives P = Rs.59,000.

Given the capitals of A and B are in the ratio 7:9. A withdraws after 8 months, and the profit ratio is 8:9. Let B's capital be used for x months. The profit ratio is proportional to capital × time, so: A's contribution = 7 × 8 = 56 B's contribution = 9 × x Given profit ratio A:B = 8:9, so: 56 : 9x = 8 : 9 Cross-multiplied: 56 × 9 = 8 × 9x 504 = 72x x = 7 months Therefore, B's capital was used for 7 months, which corresponds to option D.

Options B (Trap), D (Dart), and A (Part) are anagrams of each other, as they contain the same letters rearranged (p, a, r, t). Option C (Cart) contains a different letter 'c' instead of 'p' or 'd', so it is not an anagram of the others. Therefore, 'Cart' is the odd one out.

Options A (GFI), C (LKN), and D (YXA) each have letters arranged in a pattern where the middle letter is alphabetically one position before the first letter, and the third letter is alphabetically one position after the first letter, forming a pattern of 'first letter - 1, first letter, first letter + 1' with some skips. Specifically, LKN and YXA show a clear descending pattern with one letter skipped between letters. Option B (QOR) does not follow this pattern as the letters are not in a consistent ascending or descending order relative to each other. Therefore, B does not belong to the group.

Option C (4242) is the only number in the group that does not have two identical pairs of digits in sequence. Options A (4422), B (2442), and D (2244) each contain two pairs of identical digits grouped together, while C alternates digits without forming such pairs.

A invests Rs.1200 for 12 months, so his investment-months = 1200 × 12 = 14400. B joins after 3 months, so B's investment is for 9 months. Let B's investment be x, so investment-months = 9x. C joins after 6 months, so C's investment is for 6 months. Let C's investment be y, so investment-months = 6y. The profit ratio 2:3:5 corresponds to the investment-months ratio 14400 : 9x : 6y = 2 : 3 : 5. From 14400/2 = 9x/3 = 6y/5, we get 14400/2 = 7200, so 9x/3 = 7200 which gives 3x = 7200, hence x = 2400. Therefore, B's investment is Rs.2400, which corresponds to option A.

The profit share is proportional to the product of investment and time. A invested Rs.25000 for 12 months, B Rs.30000 for 12 months, and C Rs.35000 for 8 months (since C joined after 4 months). Calculating shares: A=25000*12=300000, B=30000*12=360000, C=35000*8=280000. Total=940000. C's share = (280000/940000)*47000 ≈ Rs.14000. However, the calculation shows Rs.14000, which matches option D, so the original answer D is correct. Rechecking calculations: 280000/940000=0.2979; 0.2979*47000=13999 ≈ Rs.14000. So the original answer D is correct. The initial explanation was missing, so it has been added.

A's investment for 12 months is 70000 × 12 = 840000; B's investment for 6 months is 120000 × 6 = 720000. The ratio of their investments is 840000:720000 = 7:6. Total profit is Rs. 52000, so B's share = (6/13) × 52000 = Rs. 24000. However, this contradicts the options given. Rechecking: 7 + 6 = 13 parts; B's share = (6/13)*52000 = Rs. 24000, which matches option B. Therefore, the original correct answer B is correct. The initial calculation was correct; the explanation confirms B's share is Rs. 24000.