Mathematics

P's annual salary is Rs. 5000 × 12 = Rs. 60,000. The total profit is Rs. 2,00,000. After paying P's salary, the remaining profit to be shared is Rs. 2,00,000 - Rs. 60,000 = Rs. 1,40,000. The profit is shared in the ratio of their investments, which is 4 lakhs : 10 lakhs = 2 : 5. So, P's share of the profit is (2/7) × 1,40,000 = Rs. 40,000 and Q's share is (5/7) × 1,40,000 = Rs. 1,00,000. Therefore, P's total earning = salary + profit share = 60,000 + 40,000 = Rs. 1,00,000 and Q's total earning = Rs. 1,00,000. Hence, the ratio of their earnings is 1,00,000 : 1,00,000 = 1 : 1. So, the correct answer is option D.

All four numbers (104, 108, 110, 112) are even and thus divisible by 2. For divisibility by 4, the last two digits must form a number divisible by 4. 104 (last two digits 04), 108 (08), and 112 (12) are divisible by 4, but 110 (10) is not divisible by 4. For divisibility by 8, the last three digits must be divisible by 8. 104 and 112 are divisible by 8, but 108 and 110 are not. Therefore, 110 is the only number not divisible by 4 and 8, making it the odd one out.

The profit sharing ratio in a partnership depends on the product of the capital invested and the time for which it is invested. Here, A invests Rs. 40,000 for 3 years, so the product is 40,000 × 3 = 120,000. B invests Rs. 80,000 for 1 year and then Rs. 40,000 for 2 years (after withdrawing Rs. 40,000 at the end of the first year), so the product is (80,000 × 1) + (40,000 × 2) = 80,000 + 80,000 = 160,000. C invests Rs. 1,20,000 for 2 years and then Rs. 40,000 for 1 year (after withdrawing Rs. 80,000 at the end of the second year), so the product is (1,20,000 × 2) + (40,000 × 1) = 240,000 + 40,000 = 280,000. The ratio of their investments by time is therefore 120,000 : 160,000 : 280,000, which simplifies to 12 : 16 : 28, and further to 3 : 4 : 7. This matches option B, so the correct answer is B.

Let B's investment be x. A's investment share = 16000 × 8 = 128000 B's investment share = x × 4 = 4x Now, B claims 2/7 of total profit, so we write the equation: 4x divided by (128000 + 4x) = 2/7 Cross multiplying: 7 × 4x = 2 × (128000 + 4x) 28x = 256000 + 8x 28x minus 8x = 256000 20x = 256000 x = 256000 divided by 20 x = Rs. 12,800 So B contributed Rs. 12,800, which is Option B.

The odd one out is 426 because in each of the other numbers the leading digit is followed by its perfect square—5 → 25 gives 525, 3 → 9 gives 39, and 2 → 4 gives 24—whereas 426's trailing digits 26 are not the square of the leading digit 4 (4² = 16), breaking the pattern. This pattern is a common reasoning for such odd one out questions involving numbers.

Options A, B, and C each consist of letters that follow a consistent alphabetical pattern (every second or third letter), while option D contains letters forming a word 'CHEM', which breaks the pattern and does not belong to the group.

A's share of profit is 2/3. The increase in profit rate from 5% to 7% causes A's income to increase by Rs.200, which corresponds to 2% of A's capital share. Calculating A's capital from this, then using profit shares to find B's capital, we find B's capital is Rs.3600.

Option A (11) is the only prime number in the group, while the others (28, 327, 416) are composite numbers. Therefore, 11 does not belong to the group.

All the numbers 508, 328, 608, and 148 are even and divisible by 4 since their last two digits (08, 28, 08, and 48 respectively) are multiples of 4. To find the odd one out, we need a different property. Checking divisibility by 8, 608 is divisible by 8 (last three digits 608 ÷ 8 = 76), 148 is not divisible by 8 (last three digits 148 ÷ 8 = 18.5), 508 is divisible by 4 but not by 8 (508 ÷ 8 = 63.5), and 328 is divisible by 8 (328 ÷ 8 = 41). So 148 is the only number not divisible by 8, making it the odd one out.

The rent should be divided in proportion to the product of the number of horses and the months each person kept them. A's share is 12×8=96, B's share is 16×9=144, and C's share is 18×6=108. Total = 96+144+108=348. C's share of the rent = (108/348)×870 = Rs.270.