Mathematics

To find the sum of 4 arithmetic means between 18 and 3, we consider the arithmetic sequence formed by 6 terms: 18, four arithmetic means, and 3. The common difference d = (3 - 18) / 5 = -3. The four arithmetic means are 15, 12, 9, and 6. Their sum is 15 + 12 + 9 + 6 = 42. Therefore, the correct answer is option C (42).

A ratio equivalent to 3:7 must have terms in the same proportion. Multiplying both terms of 3:7 by 3 gives 9:21, which is option C. Options A and B do not maintain the same ratio.

The computer depreciates by 10% annually, so after one year its value is 90% of 100,000 = 90,000. After the second year, it is 90% of 90,000 = 81,000. Therefore, the value after two years is Rs. 81,000.

The arithmetic mean of two numbers is their sum divided by 2. Here, (x-3 + x+3)/2 = (2x)/2 = x, so the mean is x.

The statements 'a > b' and 'b > a' cannot both be true simultaneously for any real numbers a and b. Therefore, none of the given options correctly describe the situation, making 'None of these' the correct choice.

From the given, (x/100)*y = 100 and (y/100)*z = 200. From the first, y = 10000/x. Substitute into the second: (10000/x)/100 * z = 200, which simplifies to (100*z)/x = 200, so z = 2x. Therefore, the relation is Z = 2X.

The arithmetic mean between two numbers a and b is calculated as (a + b) / 2, which is option A. This is the standard formula for the arithmetic mean.

To cover 28 miles in 30 minutes (which is 0.5 hours), the speed required is calculated by dividing the distance by the time: speed = 28 miles ÷ 0.5 hours = 56 mph. Therefore, the correct answer is option C (56 mph). The original question had the correct calculation in the explanation but incorrectly marked option D as the correct answer. This has been corrected to option C.

Let the number of boys be x and the number of girls be 150 - x. Given that the number of girls is x% of the total students, so 150 - x = (x/100) * 150. Solving this equation gives x = 65.

If A's income is 25% more than B's income, then A = 1.25 × B. To express B's income in terms of A's income, rearrange the equation: B = A ÷ 1.25 = 0.8 × A. This means B's income is 80% of A's income. Therefore, the correct answer is option B (80%).

The banker's discount (BD) is calculated using the formula BD = True Discount (TD) × (Face Value / (Face Value - TD)). Here, TD = 90 and Face Value = 540. So, BD = 90 × (540 / (540 - 90)) = 90 × (540 / 450) = 90 × 1.2 = 108. Hence, option B is correct.

Ali bought the table for Rs 1000 and sold it for Rs 800, so the loss is Rs 200. The percentage loss is (Loss / Cost Price) × 100 = (200 / 1000) × 100 = 20%.

The car's price is Rs. 3,25,000. It was insured for 85% of its price, which is Rs. 2,76,250. The insurance company paid 90% of the insured amount, which is Rs. 2,48,625. The difference between the car's price and the amount received is Rs. 3,25,000 - Rs. 2,48,625 = Rs. 76,375. This matches option C, so the correct answer is C.

Sam's work rate is 1/4 job per day, Lisa's is 1/6, and Tom's is 1/2. Combined, their rate is 1/4 + 1/6 + 1/2 = 0.25 + 0.1667 + 0.5 = 0.9167 jobs per day. The time to complete one job together is 1 / 0.9167 ≈ 1.09 days.

Banker's gain is the difference between the true discount and the banker's discount. Given the banker's gain is Rs 24, and the rate is 10% for 2 years, the present worth can be calculated as Rs 500. Hence, option B is correct.

Each animal has one head, so hens + cows = 48. Hens have 2 feet and cows have 4 feet, so 2*hens + 4*cows = 140. Solving these equations gives hens = 24 and cows = 24.

To find the number to add to 11.138 to make it divisible by 77, first find the remainder when 11,138 is divided by 77. 11,138 ÷ 77 gives a remainder of 69. Since 77 - 69 = 8, adding 8 to 11,138 makes it divisible by 77 exactly.

When the price of sugar increases by 20%, the price factor becomes 1.20. When consumption decreases by 25%, the consumption factor becomes 0.75. The new expenditure is the product of these two factors: 1.20 × 0.75 = 0.90, which means the expenditure is 90% of the original expenditure. This is a 10% decrease in expenditure. Therefore, the family's expenditure on sugar decreases by 10%.

When the tax increases by 20%, the price becomes 120% of the original. Consumption decreases by 20%, so quantity is 80% of original. Expenditure = price × quantity = 1.2 × 0.8 = 0.96, which is a 4% decrease from the original expenditure.

After 2 hours, the first plane travels 150 mph × 2 = 300 miles north, and the second plane travels 200 mph × 2 = 400 miles west. Using the Pythagorean theorem, the distance apart is √(300² + 400²) = √(90000 + 160000) = √250000 = 500 miles.

If the price increases by 20%, the new price is 120% of the original. To keep expenditure the same, consumption must be reduced to 100/120 = 5/6 of original, which is a reduction of (1 - 5/6) × 100% = 16.66%.

Total votes = 7500; invalid votes = 20% of 7500 = 1500; valid votes = 7500 - 1500 = 6000. One candidate got 55% of valid votes = 0.55 × 6000 = 3300. The other candidate got the remaining valid votes = 6000 - 3300 = 2700. However, 2700 is option A, but the question asks for the number of valid votes the other candidate got, which is 2700. The original correct_answer was A, which matches 2700, so the original answer is correct. The explanation was missing and is now provided. The difficulty is set to easy as it involves basic percentage calculations.

Revenue is calculated as Price × Quantity. When the price of TV sets is increased by 30%, the new price becomes 1.3 times the original price. When sales decrease by 20%, the quantity sold becomes 0.8 times the original quantity. Therefore, the new revenue is 1.3 × 0.8 = 1.04 times the original revenue, which means revenue increases by 4%. Hence, the effect on the revenue receipts of the shop is a 4% increase.

The sum of the known numbers is 6999 + 8888 + 777 = 16664. To find the missing number, subtract this sum from 19700: 19700 - 16664 = 3036. However, the options given (36, 16, 64, 26) do not include 3036. The question as stated is inconsistent with the options. The search results show a similar question but with 9999 instead of 6999, where the missing number is 36. Assuming the intended question was 9999 + 8888 + 777 + ? = 19700, the missing number is 36, which corresponds to option A. Therefore, the question and options should be corrected to use 9999 instead of 6999, making the correct answer A (36).

Let the total number of votes polled be x. Valid votes = x - 68. The winner gets 52% of valid votes, and the loser gets 48%. The difference is 4% of valid votes, which equals 98 votes. So, 0.04(x - 68) = 98, solving gives x = 2382.