Mathematics

When the side of a square is increased by 25%, the new side length is 1.25 times the original. The area increases by (1.25)^2 - 1 = 1.5625 - 1 = 0.5625, or 56.25%.

The loss is Rs.600 - Rs.500 = Rs.100. Loss percent = (Loss / Cost Price) × 100 = (100 / 600) × 100 = 16 2/3%.

Ramees sells 900 grams of goods but charges for 1 kilogram (1000 grams) at cost price. The gain arises because he gives less quantity but charges for the full kilogram. The gain percent is calculated as ((1000 - 900) / 900) × 100 = (100 / 900) × 100 = 11 1/9%. This matches option C, not B as originally stated.

Let the two numbers be x and y. Given x + y = 2490 and 6.5% of x = 8.5% of y, which means 0.065x = 0.085y. From this, x/y = 0.085/0.065 = 17/13. Using x + y = 2490 and x = (17/13)y, solving gives y = 1479 and x = 1011. Hence, the numbers are 1011 and 1479, matching option B.

When a number is increased by 10%, it becomes 1.1 times the original. Then reducing this new number by 10% multiplies it by 0.9, resulting in 1.1 × 0.9 = 0.99 times the original number, which is a 1% decrease.

If the price increases by 25%, the new price is 125% of the original. To keep expenditure constant, consumption must be reduced so that (new price) × (new consumption) = (original price) × (original consumption). Let the reduction be x%. Then, (1 + 0.25) × (1 - x) = 1, so 1.25 × (1 - x) = 1, which gives 1 - x = 1/1.25 = 0.8, so x = 0.2 or 20%. However, this is a common misconception. The correct approach is to find the percentage decrease in consumption as (increase%)/(1 + increase%) = 25/125 = 0.2 or 20%. So the correct answer is 20%. The original answer D (20%) is correct, but the explanation was missing. Therefore, the correct answer is D, not B.

Given: 5% of A's income = 15% of B's income, so A = 3B. Also, 10% of B's income = 20% of C's income, so B = 2C. Given C = Rs. 2000, B = 2 × 2000 = Rs. 4000, and A = 3 × 4000 = Rs. 12000. Total income = A + B + C = 12000 + 4000 + 2000 = Rs. 18000. However, this contradicts the calculation; rechecking: 5% A = 15% B → A = (15/5)B = 3B; 10% B = 20% C → B = (20/10)C = 2C; with C=2000, B=4000, A=12000; total = 12000+4000+2000=18000. The correct total is Rs. 18000, which corresponds to option C. Therefore, the original correct_answer 'C' is correct. The initial confusion was in the explanation step. The explanation now clearly supports option C.

The dealer uses 800 grams instead of 1000 grams but charges for 1000 grams, effectively selling 800 grams for the price of 1000 grams. The gain percent is ((1000 - 800) / 800) × 100 = 25%.

Let A be the set of students who failed in English and B be the set of students who failed in Mathematics. Given n(A) = 50, n(B) = 30, and n(A ∩ B) = 12. The number of students failing in at least one subject is n(A ∪ B) = n(A) + n(B) - n(A ∩ B) = 50 + 30 - 12 = 68. Therefore, the number of students passing both subjects is the total number of students minus those failing at least one subject: 100 - 68 = 32. Hence, the correct answer is 32 (option D).

Let the original price per kg be x. At original price, quantity bought for Rs.800 is 800/x kg. After 25% reduction, price is 0.75x, so quantity bought is 800/(0.75x) = (800/0.75)/x = (1066.67)/x kg. The increase in quantity is 5 kg, so (1066.67/x) - (800/x) = 5, which simplifies to (266.67)/x = 5, giving x = 53.33. The reduced price is 75% of original, so 0.75 * 53.33 = Rs.40. However, this contradicts the options and the calculation. Rechecking: Let original price = p. Then quantity originally = 800/p. After reduction, price = 0.75p, quantity = 800/(0.75p) = (800/0.75)/p = (1066.67)/p. Increase in quantity = 5, so (1066.67)/p - 800/p = 5 => (266.67)/p = 5 => p = 266.67/5 = 53.33. Reduced price = 0.75 * 53.33 = 40. So reduced price is Rs.40, which matches option C. Therefore, the original answer C is correct. Explanation updated accordingly.

The trader buys the car at 20% discount, so the buying price is 80% of the original price. He sells it at 40% more than the buying price, which is 1.4 × 80% = 112% of the original price. Therefore, the profit is 12% of the original price.

The total cost is Rs.840. One-fourth (Rs.210) is sold at 20% loss, so selling price = 210 - 20% of 210 = Rs.168. To gain 20% overall, total selling price should be 840 + 20% of 840 = Rs.1008. The remainder cost is Rs.630, so selling price needed = 1008 - 168 = Rs.840. Gain on remainder = (840 - 630)/630 = 33 1/3%.

Let the cost price be Rs. x. Selling at Rs. 800 causes a loss of (x - 800). Selling at Rs. 980 causes a gain of (980 - x), which is double the loss: 980 - x = 2(x - 800). Solving gives x = Rs. 875.

The total votes cast are 1136 + 7636 + 11628 = 20400. The winning candidate received 11628 votes. The percentage of total votes received by the winning candidate is (11628 / 20400) × 100 ≈ 57%. Since 57% is not among the given options (11.6%, 60%, 76.4%), the correct choice is 'None of these'.

The gain is equal to the selling price of 30 mangoes when selling 150 mangoes. Gain percent = (Gain / Cost Price) × 100. Cost price of 150 mangoes = Selling price of 150 mangoes - Gain = Selling price of 150 mangoes - Selling price of 30 mangoes = Selling price of 120 mangoes. Therefore, gain percent = (30 / 120) × 100 = 25%.

Let the original price be Rs. x per kg. At original price, quantity bought = 385/x kg. After 20% reduction, price = 0.8x, quantity bought = 385/0.8x = 385/(0.8x) kg. The increase in quantity = 385/(0.8x) - 385/x = 3.5 kg. Solving gives x = Rs. 25 per kg.

The plant depreciates by 10% annually, so after 1 year its value is 100000 × 0.9 = 90000. After 2 years, it is 90000 × 0.9 = 81000. Hence, the value after 2 years is Rs. 81000.

Given 60% employees are men, and 40% of men earn more than Rs. 50,000, so men earning >50,000 = 0.6 * 0.4 = 24%. Total employees earning >50,000 is 36%, so women earning >50,000 = 36% - 24% = 12%. Since women are 40% of employees, women earning less than Rs. 50,000 = 40% - 12% = 28%, which is 70% of women (28%/40% = 0.7 or 70%). Therefore, 70% of women earn less than Rs. 50,000 per year.

Let the cost of the book sold at a loss be x. Then the other book costs 480 - x. Both are sold at the same price. The selling price of the first book is x - 15% of x = 0.85x. The selling price of the second book is (480 - x) + 19% of (480 - x) = 1.19(480 - x). Equating the selling prices: 0.85x = 1.19(480 - x). Solving gives x = Rs.140.

If the cost price (C.P) of 15 books equals the selling price (S.P) of 18 books, then the selling price of one book is (C.P of 15 books) / 18. The cost price of one book is (C.P of 15 books) / 15. Comparing these, the selling price per book is less than the cost price per book, indicating a loss. Calculating the loss percentage: Loss% = [(C.P - S.P) / C.P] × 100 = [(15/15 - 15/18) / (15/15)] × 100 = (1 - 5/6) × 100 = (1/6) × 100 = 16 2/3% loss. However, since the selling price per book is less than the cost price, the loss is 16 2/3%. The correct answer is A.

When the length of a rectangle is increased by 40% and the width is decreased by 20%, the new area is calculated by multiplying the new length factor and the new width factor: (1 + 0.40) × (1 - 0.20) = 1.40 × 0.80 = 1.12. This means the new area is 1.12 times the original area, which corresponds to a 12% increase in area. Therefore, the correct answer is that the area has increased by 12%.

Given AB = 5 cm, AC = 3 cm, so CB = 2 cm. Increasing AC by 6% means AC_new = 3 × 1.06 = 3.18 cm. Since AB is fixed, CB_new = 5 - 3.18 = 1.82 cm. The decrease in CB is 2 - 1.82 = 0.18 cm. The percentage decrease in CB is (0.18 / 2) × 100% = 9%. Therefore, the correct answer is 9%, which corresponds to option D.

The ratio of Faheem's salary to Imran's salary to Naveed's salary is calculated by dividing each salary by the greatest common divisor. The salaries are 80,000, 70,000, and 50,000 rupees respectively. Dividing each by 10,000 gives 8:7:5, which matches option B.

The cost price of one pen is Rs.9/8 = Rs.1.125. The selling price of one pen is Rs.8/9 ≈ Rs.0.8889. Since the selling price is less than the cost price, there is a loss. The loss percentage = ((1.125 - 0.8889)/1.125) × 100 ≈ 20.98%.

The selling price of each bicycle is Rs.990. For the first bicycle, with a 10% profit, cost price = 990 / 1.1 = Rs.900. For the second bicycle, with a 10% loss, cost price = 990 / 0.9 = Rs.1100. Total cost = 900 + 1100 = Rs.2000. However, this contradicts the options, so rechecking: 10% profit means SP = 110% of CP, so CP = SP / 1.1 = 900; 10% loss means SP = 90% of CP, so CP = SP / 0.9 = 1100; total cost = 900 + 1100 = Rs.2000. Option A is Rs.2000, so correct answer is A, not B. Correction made accordingly.