Mathematics

A and B together complete the work in 15 days, so their combined work rate is 1/15 per day. B alone completes the work in 20 days, so B's work rate is 1/20 per day. Therefore, A's work rate is (1/15 - 1/20) = (4/60 - 3/60) = 1/60 per day, meaning A alone can complete the work in 60 days. However, since 60 is option A, the correct answer should be A, not D. Rechecking the calculation: A's rate = 1/15 - 1/20 = (4/60 - 3/60) = 1/60, so A alone takes 60 days. Therefore, correct answer is A.

If 10% of the workers were fired, then 90% remained. Since 540 workers survived, 90% corresponds to 540. Therefore, the total number of workers originally = 540 ÷ 0.9 = 600.

Let Arif's share be x. Hafiz's share is 4x, and Arif's share is one-third of Haider's, so Haider's share is 3x. Total share: x + 4x + 3x = 8x = 2560, so x = 2560/8 = 320. Therefore, Arif's share is Rs 320.

The total age of A, B, C, D, and E is 40 × 5 = 200 years. The total age of A and B is 35 × 2 = 70 years, and the total age of C and D is 42 × 2 = 84 years. Therefore, the age of E = 200 - (70 + 84) = 46 years. However, since 46 is option B, the correct answer is B, not A. Correction: The age of E is 46 years, which corresponds to option B.

If 10 men take 12 days to complete the work, the total work is 10 × 12 = 120 man-days. With 12 men working, the time taken is 120 ÷ 12 = 10 days. However, the calculation shows 10 days, which matches option B, so let's recheck carefully. Actually, 10 men × 12 days = 120 man-days. For 12 men, days = 120 ÷ 12 = 10 days. So the correct answer is B, not C. The original correct_answer was 'X', which is invalid. The correct answer is B (10 days).

Let the original cost price be 100. With 20% profit, the original selling price is 120. After a 25% increase, the new selling price is 120 × 1.25 = 150. The new profit percentage is 25%, so the new cost price must satisfy: cost price × 1.25 = 150, giving cost price = 120. The cost price increased from 100 to 120, which is a 20% increase. However, this contradicts the options, so let's re-check: The new profit is 25%, so new cost price × 1.25 = new selling price = 150. Thus, new cost price = 150 / 1.25 = 120. The increase in cost price is from 100 to 120, which is 20%. But the options list 20% as A, so correct answer is A. Therefore, correct answer is A (20%).

The total price of the land is Rs. 6 crore 75 lakhs, which equals Rs. 6.75 crore or Rs. 67,500,000. A 2% commission on this amount is 0.02 × 67,500,000 = Rs. 1,350,000, which corresponds to option A.

The pattern in the series is that the differences between consecutive terms increase by 4 each time: 5-2=3, 12-5=7, 23-12=11, 38-23=15, 57-38=19. The next difference should be 23 (19 + 4), so the next number is 57 + 23 = 80. Therefore, the correct answer is C (80).

The number series follows the pattern where each term is obtained by multiplying the previous term by 3 and then subtracting 3. Specifically, aₙ₊₁ = 3 × aₙ - 3. Starting with 3: 3 × 3 - 3 = 6, 3 × 6 - 3 = 15, 3 × 15 - 3 = 42, 3 × 42 - 3 = 123, and 3 × 123 - 3 = 366. Therefore, the missing number in the series is 42 (option C).

The first person completes 1/10 of the work per day, and the second person completes 1/15 per day. Together, they complete 1/10 + 1/15 = 1/6 of the work per day, so they finish the work in 6 days.