Mathematics

Let the original cost price be Rs. x. The selling price at 10% loss is 0.9x. If the cost price was 20% less, it would be 0.8x, and selling at Rs. 75 less means selling price is 0.9x - 75. This new selling price is 25% gain on 0.8x, so 0.9x - 75 = 1.25 * 0.8x = 1.0x. Solving 0.9x - 75 = x gives x = Rs. 250.

Let the original fraction be $\frac{x}{y}$. Increasing the numerator by 250% means the new numerator is $x+2.5x=3.5x$. Increasing the denominator by 400% means the new denominator is $y+4y=5y$. The new fraction is $\frac{3.5x}{5y}=\frac{7}{19}$. Cross-multiplying gives $3.5x\times 19=7\times 5y$, or $66.5x=35y$, which simplifies to $\frac{x}{y}=\frac{35}{66.5}=\frac{5}{9}$. Thus, the original fraction is $\frac{5}{9}$.

If Haroon uses 25% more petrol every day, his daily consumption increases to 1.25 times the original daily consumption. Originally, the tank lasts 10 days at the original consumption rate. The total petrol in the tank is equivalent to 10 days' worth of the original daily consumption. With the increased consumption, the number of days the tank will last is the total petrol divided by the new daily consumption: 10 ÷ 1.25 = 8 days. Therefore, the tank will last 8 days, which corresponds to option D.

Let Y's pay be Rs. y. Then X's pay is 120% of y, i.e., 1.2y. The total pay is y + 1.2y = 2.2y = 550. Solving for y gives y = 550 / 2.2 = 250. Hence, Y is paid Rs. 250 per week.

Using the principle of inclusion-exclusion, the percentage reading at least one magazine is 45% + 55% + 40% - 30% - 15% - 25% + 10% = 80%. Therefore, 20% do not read any magazine.

Let the total percentage of students be 100%. Given 18% play neither football nor cricket, so 82% play football or cricket or both. Using the formula for union of two sets: P(F ∪ C) = P(F) + P(C) - P(F ∩ C), we have 82% = 40% + 50% - P(F ∩ C). Solving gives P(F ∩ C) = 8%.

Using the formula for union of two sets: P(Car or Mobile) = P(Car) + P(Mobile) - P(Both) = 80% + 60% - 55% = 85%. Therefore, 85% of those surveyed owned a car or a mobile phone or both.

Starting with 17xy + 7 = 19xy, subtract 17xy from both sides to get 7 = 2xy. Dividing both sides by 2 gives xy = 7/2. Multiplying both sides by 4 gives 4xy = 4 * (7/2) = 14. However, since the options do not include 14 as the correct answer for 4xy, let's re-examine. The original equation is 17xy + 7 = 19xy. Subtract 17xy: 7 = 2xy, so 2xy = 7, then xy = 7/2. Then 4xy = 4 * (7/2) = 14, which matches option D. Therefore, the correct answer is D, not A. The initial correction was incorrect. The original correct_answer D is correct. Explanation updated accordingly.

First, calculate the rebate: 6% of Rs. 6650 = Rs. 399. So, the price after rebate = 6650 - 399 = Rs. 6251. Then, calculate sales tax: 10% of Rs. 6251 = Rs. 625.10. Total amount to pay = 6251 + 625.10 = Rs. 6876.10.

Given that 8% of the voters did not cast their votes, 92% of the total voters actually voted. The winner obtained 48% of the total votes, so the loser got 44% (92% - 48%) of the total votes. The difference between the winner and the loser is 4% of the total voters, which equals 1100 votes. Therefore, the total number of voters is 1100 divided by 0.04, which equals 27,500. This matches option D, making it the correct answer.