Study HubHubPage 175/182Scan verified MCQs with the answer highlighted, then open explanations when you want the reasoning.
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Simple Interest/Discount
The banker's gain on a certain sum due 2 years hence at 10% per annum is Rs 24. What is the present worth?
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.
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Time and Work
If Sam can do a job in 4 days, Lisa can do it in 6 days, and Tom can do it in 2 days, how long would it take if Sam, Lisa, and Tom worked together to complete the job?
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.
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Insurance/Percentage
The price of a car is Rs. 3,25,000. It was insured for 85% of its price. The car was completely damaged in an accident, and the insurance company paid 90% of the insured amount. What was the difference between the price of the car and the amount received?
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.
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Percentage
Ali sold a table for Rs 800 which he bought for Rs 1000. What is his percentage loss?
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%.
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Bills/Discount
The true discount on a bill of Rs. 540 is Rs. 90. The banker's discount is:
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.
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Percentage
A's income is 25% more than B's income. What is B's income in terms of A's income?
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%).
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Algebra/Percent
The sum of the number of boys and girls in a school is 150. If the number of boys is x, then the number of girls is x% of the total number of students. What is the number of boys?
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.
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Speed and Distance
John is travelling to a meeting that is 28 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?
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.
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Arithmetic Mean
A single arithmetic mean between a and b is:
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.
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Algebra
If x% of y is 100 and y% of z is 200, then find the relation between x and z.
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.