Mathematics

30% of the number equals 12.6, so the number can be found by dividing 12.6 by 0.30, which gives 42.

The basic hourly rate is Rs. 2000/40 = Rs. 50. Overtime rate is 25% above Rs. 50, which is Rs. 62.5 per hour. Let the overtime hours be x. Total wage = 2000 + 62.5x = 2500, so 62.5x = 500, x = 8 hours. Total hours = 40 + 8 = 48 hours. However, the calculation shows 8 overtime hours, so total hours should be 48, which corresponds to option C. Rechecking the calculation confirms option C is correct.

First, calculate 15% of 201: 0.15 × 201 = 30.15. Then divide 199.54 by 30.15: 199.54 ÷ 30.15 ≈ 6.62. This value does not match any of the given options. However, the search results indicate the calculation yields approximately 6.62, which is not close to any of the options 41, 42, 43, or 44. The original options seem incorrect for the question as stated. If the question intended to ask "What is 199.54 divided by 7.54?" (where 7.54 is 15% of 50.27), the answer would be close to 26.5, but this is not the case here. Given the options, the closest reasonable answer to the calculation 199.54 ÷ 4.75 (which is 15% of 31.67) would be around 42, but this is speculative. Therefore, the question or options need correction. Since none of the options match the correct calculation, the best correction is to update the options to include the correct approximate answer 6.62, which rounds to 7. The closest option to 6.62 is 7, so the options should be corrected accordingly. For the current options, none is correct. To align with the original options, if the question is changed to "What is 199.54 divided by 4.75?" (which is 15% of 31.67), the answer is approximately 42, which matches option B. But this is a different question. Hence, the correct answer for the original question is approximately 6.62, which is not among the options. The best fix is to change the correct answer to A (41) and update the question to "What is 199.54 divided by 4.75?" to match the options and answer. However, since the original question is "What is 199.54 divided by 15% of 201?", the correct answer is approximately 6.62, which is not among the options. Therefore, the correct answer should be none of the above, but since that is not an option, the question and options are inconsistent. The verified correct answer to the original question is approximately 6.62, which is not listed. The best option to select is A (41) if forced to choose, but this is not mathematically accurate. The question needs revision for clarity and correct options.

XCIX in Roman numerals represents 99 because XC means 90 (100 - 10) and IX means 9 (10 - 1), so together they form 99.

If the length is reduced to 3/5 of its original length and the width remains the same, the new area is (3/5) times the original area. Therefore, the ratio of original area to reduced area is 1 : 3/5, which simplifies to 5 : 3. However, since the width is not mentioned as changed, the ratio of original area to reduced area is 5:3, matching option A. But option A is 5:3, which is correct. So correct answer is A, not C. Rechecking: Original area = L × W; Reduced area = (3/5)L × W = (3/5) original area; Ratio original to reduced = 1 : 3/5 = 5/3 : 1 = 5:3. So correct answer is A.

The discount amount is Rs.600,000 - Rs.570,000 = Rs.30,000. To find the percentage discount, divide the discount amount by the original price and multiply by 100: (30,000 / 600,000) × 100 = 5%. Therefore, the percentage discount Mr. Aslam received is 5%, which corresponds to option A.

Let the price of a chair be C and the price of a table be T. From the first equation, 2C + T = 400. From the second, C + T = 300. Subtracting the second from the first gives C = 100. Substituting back, 100 + T = 300, so T = 200.

One nautical mile per hour is defined as one knot. Therefore, 1 nautical mile per hour equals exactly 1 knot.

The distance covered at 6 km/hr in 50 minutes (which is 5/6 hour) is 6 × 5/6 = 5 km. At 10 km/hr, time taken to cover 5 km is 5/10 = 0.5 hours or 30 minutes. However, since 30 minutes is option B, let's recheck calculations carefully: Distance = speed × time = 6 km/hr × (50/60) hr = 6 × 5/6 = 5 km. Time at 10 km/hr = distance/speed = 5/10 = 0.5 hr = 30 minutes. So the correct answer is B, not C. Therefore, correct_answer is B and explanation adjusted accordingly.

The total man-hours required to paint the house is calculated by multiplying the number of workers by the hours they work: 325 workers × 8 hours = 2600 man-hours. To complete the same job in one day with only 8 workers, the total hours needed per worker is 2600 man-hours ÷ 8 workers = 325 hours. Since the question asks how many hours 8 workers should work in one day to finish the job, the mathematically correct answer is 325 hours, which is not among the options provided. However, given the options, none are correct for the problem as stated. The original answer choice 'D' (13 hours) is incorrect based on the calculation. The question or options appear flawed or ambiguous. The correct calculation is 325 hours, but since this is not an option, the question should be revised for clarity or options corrected. For now, the correct answer based on the problem is 325 hours, which is not listed.