Arithmetic Study Resources for Competitive Exams

Arithmetic

Averages Mixtures & Alligation Partnerships Percentages Pipes & Cisterns Profit, Loss & Discount Ratio & Proportion Simple & Compound Interest Time & Work Time, Speed & Distance

Q. If a solution contains 25% sugar, how much sugar is in 40 liters of the solution?

A. 5 liters
B. 10 liters
C. 15 liters
D. 20 liters

Solution

25% of 40 liters = 0.25 * 40 = 10 liters of sugar.

Correct Answer: B — 10 liters

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Q. If a solution is made by mixing 3 parts of liquid A and 5 parts of liquid B, what is the ratio of liquid A to the total mixture?

A. 3:8
B. 3:5
C. 5:3
D. 5:8

Solution

Total parts = 3 + 5 = 8. Ratio of A = 3:8.

Correct Answer: A — 3:8

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Q. If a solution is made by mixing 30% and 70% solutions in equal volumes, what is the percentage concentration of the resulting solution?

A. 50%
B. 60%
C. 70%
D. 40%

Solution

Concentration = (30% + 70%) / 2 = 50%.

Correct Answer: B — 60%

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Q. If a solution is made by mixing 5 liters of a 20% solution with 15 liters of a 10% solution, what is the concentration of the resulting solution?

A. 15%
B. 12%
C. 10%
D. 18%

Solution

Total solute = (0.2 * 5) + (0.1 * 15) = 1 + 1.5 = 2.5 liters. Total volume = 5 + 15 = 20 liters. Concentration = (2.5/20) * 100 = 12.5%.

Correct Answer: B — 12%

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Q. If a store sells an item for $80 after applying a discount of 20%, what was the marked price?

A. $100
B. $90
C. $110
D. $120

Solution

Let the marked price be x. After a 20% discount, the selling price is x - (0.20 * x) = 0.80x. Setting this equal to $80 gives 0.80x = $80, so x = $100.

Correct Answer: A — $100

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Q. If a student answered 80% of the questions correctly in an exam and there were 50 questions in total, how many questions did the student answer correctly? (2023)

A. 35
B. 40
C. 45
D. 50

Solution

Correct answers = 80% of 50 = 0.8 * 50 = 40.

Correct Answer: B — 40

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Q. If a student answered 90 questions correctly out of 120, what percentage of questions did the student answer correctly? (2023)

A. 70%
B. 75%
C. 80%
D. 85%

Solution

Percentage correct = (90 / 120) * 100 = 75%.

Correct Answer: C — 80%

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Q. If a student answered 90 questions correctly out of 120, what percentage of questions did the student answer incorrectly?

A. 25%
B. 20%
C. 15%
D. 30%

Solution

Incorrect answers = 120 - 90 = 30. Percentage incorrect = (30/120) * 100 = 25%.

Correct Answer: B — 20%

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Q. If a student answered 90% of the questions correctly in an exam and there were 200 questions in total, how many questions did the student answer incorrectly?

A. 10
B. 15
C. 20
D. 25

Solution

The number of questions answered correctly is 90% of 200, which is 180. Therefore, the number of questions answered incorrectly is 200 - 180 = 20.

Correct Answer: C — 20

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Q. If a student answered 90% of the questions correctly in an exam of 200 questions, how many questions did the student answer incorrectly?

A. 10
B. 20
C. 15
D. 25

Solution

If 90% were answered correctly, then 10% were answered incorrectly. Therefore, the number of incorrect answers is 10% of 200, which is 20.

Correct Answer: B — 20

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Q. If a student scored 75% in English and 85% in History, and both subjects have equal weightage, what is the average percentage score?

A. 78%
B. 80%
C. 82%
D. 84%

Solution

Average percentage = (75% + 85%) / 2 = 80%.

Correct Answer: A — 78%

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Q. If a student scores 90 marks out of 120 in an exam, what is the percentage score? (2023)

A. 75%
B. 80%
C. 85%
D. 70%

Solution

Percentage score = (90/120) * 100 = 75%.

Correct Answer: C — 85%

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Q. If a sum of money doubles in 5 years at simple interest, what is the rate of interest per annum?

A. 10%
B. 20%
C. 15%
D. 25%

Solution

The formula for simple interest is A = P(1 + rt). If the amount doubles, A = 2P. Therefore, 2P = P(1 + r*5). Simplifying gives r = 0.1 or 10%.

Correct Answer: A — 10%

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Q. If a sum of money doubles itself in 5 years at simple interest, what is the rate of interest per annum?

A. 10%
B. 12%
C. 15%
D. 20%

Solution

The formula for simple interest is A = P(1 + rt). If the amount doubles, A = 2P. Therefore, 2P = P(1 + r*5). Simplifying gives r = 0.1 or 10%.

Correct Answer: A — 10%

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Q. If a sum of money doubles itself in 5 years at simple interest, what will be the rate of interest?

A. 10%
B. 12%
C. 15%
D. 20%

Solution

Using the formula for simple interest, we know that the interest earned is equal to the principal. Therefore, if the principal doubles in 5 years, the rate of interest can be calculated as (100 * Interest) / (Principal * Time) = (100 * Principal) / (Principal * 5) = 20%. Thus, the rate of interest is 20%.

Correct Answer: A — 10%

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Q. If a sum of money doubles itself in 5 years at simple interest, what will be the rate of interest per annum?

A. 10%
B. 12%
C. 15%
D. 20%

Solution

Using the formula for simple interest, SI = PRT, where SI = Principal, R = Rate, and T = Time. If the principal doubles in 5 years, then SI = P. Therefore, P = PRT implies R = 1/5 = 20%. Hence, the rate of interest is 10%.

Correct Answer: A — 10%

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Q. If a sum of money is invested at a compound interest rate of 12% per annum, how long will it take for the investment to double?

A. 5 years
B. 6 years
C. 7 years
D. 8 years

Solution

Using the rule of 72, we estimate the time to double as 72/12 = 6 years.

Correct Answer: B — 6 years

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Q. If a sum of money is invested at a compound interest rate of 6% per annum, how much will it grow in 5 years?

A. Rs. 1349.86
B. Rs. 1200
C. Rs. 1500
D. Rs. 1600

Solution

Using A = P(1 + r)^t, A = 1000(1 + 0.06)^5 = 1000 * 1.338225 = 1338.23.

Correct Answer: A — Rs. 1349.86

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Q. If a sum of money is invested at a rate of 6% per annum, how long will it take for the investment to triple at simple interest?

A. 15 years
B. 20 years
C. 25 years
D. 30 years

Solution

Using the formula A = P(1 + rt), we have 3P = P(1 + 0.06t). Solving gives t = 20 years.

Correct Answer: B — 20 years

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Q. If a sum of money is invested at a simple interest rate of 6% per annum, how much interest will be earned on a principal of $8000 after 4 years? (1920)

A. $1920
B. $2400
C. $3200
D. $4800

Solution

Using SI = PRT, SI = 8000 * 0.06 * 4 = $1920.

Correct Answer: B — $2400

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Q. If a sum of money triples itself in 15 years at simple interest, what is the rate of interest?

A. 5%
B. 6.67%
C. 10%
D. 15%

Solution

If the sum triples, the interest earned is 2P in 15 years. Thus, 2P = PRT implies R = 2/15 = 13.33%, which is approximately 6.67%.

Correct Answer: B — 6.67%

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Q. If a sum of Rs. 1200 is invested at a compound interest rate of 5% per annum, what will be the amount after 3 years?

A. Rs. 1386.25
B. Rs. 1350
C. Rs. 1400
D. Rs. 1300

Solution

Using the formula A = P(1 + r)^t, A = 1200(1 + 0.05)^3 = 1200 * 1.157625 = 1389.15.

Correct Answer: A — Rs. 1386.25

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Q. If a trader incurs a loss of 15% on selling a bicycle for $255, what was the cost price?

A. $300
B. $280
C. $270
D. $250

Solution

Let the cost price be x. Selling Price = x - 15% of x = 255. Thus, 0.85x = 255, so x = $300.

Correct Answer: A — $300

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Q. If Partner A contributes 60% of the capital and Partner B contributes 40%, how should profits be divided if they agree to split based on capital contribution?

A. 60% to A and 40% to B
B. 50% to A and 50% to B
C. 70% to A and 30% to B
D. 40% to A and 60% to B

Solution

Profits should be divided in accordance with their capital contributions, which are 60% for A and 40% for B.

Correct Answer: A — 60% to A and 40% to B

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Q. If Partner A contributes 60% of the capital and Partner B contributes 40%, how should profits be divided if they agree to split them equally?

A. 60% to Partner A and 40% to Partner B
B. 50% to each partner
C. 70% to Partner A and 30% to Partner B
D. 40% to Partner A and 60% to Partner B

Solution

Despite the capital contribution, the partners agreed to split profits equally, hence 50% to each.

Correct Answer: B — 50% to each partner

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Q. If Partner A contributes 60% of the capital and Partner B contributes 40%, how should profits be divided if not stated otherwise?

A. Equally among partners
B. In the ratio of their capital contributions
C. Based on the time invested in the business
D. According to a pre-agreed percentage

Solution

In the absence of any other agreement, profits are typically divided in the ratio of capital contributions.

Correct Answer: B — In the ratio of their capital contributions

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Q. If Partner A contributes 60% of the capital and Partner B contributes 40%, how should profits be divided if they agree to split them based on capital contribution?

A. 60% to A and 40% to B
B. 50% to A and 50% to B
C. 70% to A and 30% to B
D. 40% to A and 60% to B

Solution

Profits should be divided in accordance with their capital contributions, so A receives 60% and B receives 40%.

Correct Answer: A — 60% to A and 40% to B

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Q. If Partner A contributes 60% of the capital and Partner B contributes 40%, how should profits be divided if they agreed to split based on capital contribution?

A. 60% to A and 40% to B
B. 50% to A and 50% to B
C. 70% to A and 30% to B
D. 40% to A and 60% to B

Solution

Profits should be divided in accordance with their capital contributions, hence 60% to A and 40% to B.

Correct Answer: A — 60% to A and 40% to B

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Q. If the amount after 2 years at compound interest is Rs. 1210 and the principal is Rs. 1000, what is the rate of interest?

A. 10%
B. 5%
C. 12%
D. 15%

Solution

Using the formula A = P(1 + r)^t, we have 1210 = 1000(1 + r)^2. Solving gives r = 0.1 or 10%.

Correct Answer: A — 10%

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Q. If the average of a set of numbers is 25 and the set contains 4 numbers, what is the total of those numbers?

A. 75
B. 100
C. 125
D. 150

Solution

Total = Average × Number of items = 25 × 4 = 100.

Correct Answer: A — 75

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Arithmetic

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