Mathematics

If the price increases by 20%, to keep expenditure constant, consumption must decrease so that (1 + price increase) × (1 - consumption decrease) = 1. Solving, consumption decrease = 20/120 = 1/6 = 16 2/3%.

The total purchase amount is Rs. 25, which includes taxable and tax-free items. The sales tax paid is Rs. 0.30, and the tax rate is 6%. To find the taxable amount before tax, divide the tax paid by the tax rate: 0.30 / 0.06 = Rs. 5. This Rs. 5 is the cost of taxable items before tax. The total cost of taxable items including tax is Rs. 5 + Rs. 0.30 = Rs. 5.30. Therefore, the cost of tax-free items is the total purchase minus the total cost of taxable items including tax: 25 - 5.30 = Rs. 19.70. Hence, the correct answer is Rs. 19.70 (Option C).

Let the cost price be Rs. x. Selling at 10% loss means selling price = 0.9x. If sold for Rs.140 more, selling price = 0.9x + 140, which equals a 4% gain, so 1.04x = 0.9x + 140. Solving gives x = Rs. 3500. However, this conflicts with options, so re-check: 1.04x - 0.9x = 140 => 0.14x = 140 => x = 1000. So cost price is Rs.1000, which matches option A. Therefore, correct answer is A.

Given the total population is 300,000 with 180,000 males, the number of females is 120,000. Since 50% of the population is illiterate, the literate population is 50% of 300,000, which is 150,000. Among males, 70% are literate, so literate males = 70% of 180,000 = 126,000. Therefore, literate females = total literate - literate males = 150,000 - 126,000 = 24,000. This matches option A.

Ram spends 65% of Rs. 720, which is 0.65 × 720 = Rs. 468. Therefore, he saves Rs. 720 - Rs. 468 = Rs. 252.

To dilute 9 ml of lotion containing 50% alcohol to a lotion containing 30% alcohol, use the dilution formula C1V1 = C2V2, where C1 = 50%, V1 = 9 ml, C2 = 30%, and V2 is the final volume after dilution. Calculating: 50% × 9 ml = 30% × V2 → 4.5 = 0.3 × V2 → V2 = 4.5 / 0.3 = 15 ml. The volume of water to add is the final volume minus the initial volume: 15 ml - 9 ml = 6 ml. Therefore, 6 ml of water should be added, which corresponds to option D.

Given that selling the house for Rs.45000 results in a gain of 1/8 of the cost price, the cost price (outlay) can be calculated as: Cost Price = Selling Price / (1 + Gain Fraction) = 45000 / (1 + 1/8) = 45000 / 1.125 = Rs.40000. To find the selling price for a 5% loss, multiply the cost price by 0.95: 40000 × 0.95 = Rs.38000. Therefore, the selling price to incur a 5% loss should be Rs.38000, which corresponds to option B.

Let the original cost price be Rs. x. The selling price with 20% profit is 1.2x. If bought at 20% less, cost price is 0.8x, and selling price is (1.2x - 75). Given this selling price yields 25% profit on 0.8x, so (1.2x - 75) = 1.25 * 0.8x = 1.0x. Solving 1.2x - 75 = x gives 0.2x = 75, so x = 375. However, this contradicts the calculation. Rechecking: 1.2x - 75 = 1.25 * 0.8x = 1.0x, so 1.2x - 75 = x, 0.2x = 75, x = 375. So original cost price is Rs.375, which matches option B. Therefore, correct answer is B. The initial explanation was missing; this explanation clarifies the solution.

Let the number of children be x. Each child receives 20% of x sweets, i.e., 0.2x sweets. Total sweets distributed = number of children × sweets per child = x × 0.2x = 0.2x². Given total sweets = 605, so 0.2x² = 605 ⇒ x² = 3025 ⇒ x = 55. Each child receives 0.2 × 55 = 11 sweets. This matches option A. Therefore, the correct answer is 11 sweets per child.

Let the selling price be S and cost price be C. Selling at 2/3 S causes a 20% loss, so (2/3)S = 0.8C, which gives C = (2/3)S / 0.8 = (5/6)S. Profit percent when selling at S is ((S - C)/C)*100 = ((S - (5/6)S)/(5/6)S)*100 = (1/6)/(5/6)*100 = (1/5)*100 = 20%. However, this contradicts the options, so rechecking: Actually, C = (2/3)S / 0.8 = (2/3)S * (1/0.8) = (2/3)S * (5/4) = (5/6)S. Profit % = ((S - C)/C)*100 = ((S - (5/6)S)/(5/6)S)*100 = (1/6)/(5/6)*100 = (1/5)*100 = 20%. So profit percent is 20%, matching option A. But option A is 20%, so correct answer is A, not B. Therefore, correct answer is A.