Arithmetic Aptitude for Competitive Exam Success

Arithmetic Aptitude

Area Average Bankers Discount Boats and Streams Calendar Chain Rule Clock Compound Interest Decimal Fraction Height and Distance Logarithm Mixture Numbers Odd Man Out and Series Partnership Percentage Permutation and Combination Pipes and Cistern Probability Problems on Ages Problems on H.C.F and L.C.M Problems on Numbers Problems on Trains Profit and Loss Races and Games Ratio and Proportion Simple Interest Simplification Square Root and Cube Root Stocks and Shares Surds and Indices Time and Distance Time and Work True Discount Volume and Surface Area

Q. A student received 75% marks in an exam. If the total marks were 800, how many marks did he score?

A. 600
B. 650
C. 700
D. 750

Solution

Marks scored = (75/100) * 800 = 600.

Correct Answer: A — 600

Q. A student scored 45 marks out of 60 in a test. What is the percentage score of the student?

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

Solution

Percentage score = (45/60)*100 = 75%.

Correct Answer: B — 75%

Q. A student scored 75% in his first exam and 85% in his second exam. If the first exam was out of 400 marks and the second out of 600 marks, what is his overall percentage?

A. 80%
B. 82%
C. 84%
D. 86%

Solution

Marks in first exam = 75% of 400 = 300. Marks in second exam = 85% of 600 = 510. Total marks = 300 + 510 = 810. Total maximum marks = 400 + 600 = 1000. Overall percentage = (810/1000) * 100 = 81%.

Correct Answer: C — 84%

Q. A student scored 75% in Mathematics and 85% in Science. If both subjects are equally weighted, what is the average percentage score?

A. 75%
B. 80%
C. 82.5%
D. 85%

Solution

Average percentage = (75 + 85) / 2 = 160 / 2 = 80%.

Correct Answer: C — 82.5%

Q. A student scored 75% in Mathematics and 85% in Science. If both subjects are of equal weight, what is the average percentage score?

A. 75%
B. 80%
C. 82.5%
D. 85%

Solution

Average percentage = (75 + 85) / 2 = 160 / 2 = 80%.

Correct Answer: C — 82.5%

Q. A student scored 75% in Mathematics and 85% in Science. If the total marks in both subjects are 200, what is the total score of the student?

A. 150
B. 160
C. 170
D. 180

Solution

Total marks in Mathematics = 75% of 100 = 75. Total marks in Science = 85% of 100 = 85. Total score = 75 + 85 = 160.

Correct Answer: B — 160

Q. A student scored 75% in Mathematics and 85% in Science. If the total marks in each subject are 200, what is the total percentage?

A. 80%
B. 82%
C. 83%
D. 85%

Solution

Total marks obtained = (0.75 * 200) + (0.85 * 200) = 150 + 170 = 320. Total percentage = (320 / 400) * 100 = 80%.

Correct Answer: B — 82%

Q. A student scored 80 marks out of 100 in a test. What is his percentage score?

A. 70%
B. 80%
C. 90%
D. 100%

Solution

Percentage = (80/100) * 100 = 80%

Correct Answer: B — 80%

Q. A student scored 80 marks out of 100 in a test. What is the percentage of marks scored?

A. 70%
B. 80%
C. 90%
D. 60%

Solution

Percentage = (80/100) * 100 = 80%

Correct Answer: B — 80%

Q. A student scored 80 marks out of 100 in Mathematics. What is the percentage of marks scored?

A. 70%
B. 80%
C. 90%
D. 60%

Solution

Percentage = (80/100) * 100 = 80%

Correct Answer: B — 80%

Q. A student scored 80% in Mathematics and 70% in Science. If the maximum marks for each subject are 100, what is the total percentage of marks obtained by the student?

A. 75%
B. 78%
C. 70%
D. 80%

Solution

Total marks obtained = 80 + 70 = 150. Total maximum marks = 200. Percentage = (150/200) * 100 = 75%.

Correct Answer: A — 75%

Q. A student scored 80% in Mathematics and 70% in Science. If the maximum marks for each subject are 100, what is the percentage of marks obtained by the student in both subjects combined?

A. 75%
B. 76%
C. 77%
D. 78%

Solution

Total marks obtained = 80 + 70 = 150. Total maximum marks = 200. Percentage = (150/200) * 100 = 75%.

Correct Answer: B — 76%

Q. A student scored 80% in Mathematics and 70% in Science. If the maximum marks for each subject are 200, what is the total percentage of marks obtained by the student?

A. 75%
B. 76%
C. 77%
D. 78%

Solution

Total marks obtained = (80/100)*200 + (70/100)*200 = 160 + 140 = 300. Total maximum marks = 200 + 200 = 400. Percentage = (300/400)*100 = 75%.

Correct Answer: B — 76%

Q. A student scored 80% in Mathematics and 70% in Science. If the total marks in each subject are 100, what is the average percentage score?

A. 75%
B. 76%
C. 77%
D. 78%

Solution

Average percentage = (80 + 70) / 2 = 150 / 2 = 75%.

Correct Answer: B — 76%

Q. A student scored 80% in Mathematics and 70% in Science. If the total marks in each subject are 200, what is the total percentage of marks obtained?

A. 75%
B. 76%
C. 77%
D. 78%

Solution

Marks in Mathematics = 0.8 * 200 = 160. Marks in Science = 0.7 * 200 = 140. Total marks = 160 + 140 = 300. Total percentage = (300 / 400) * 100 = 75%.

Correct Answer: B — 76%

Q. A student scores 60, 70, and 80 in three subjects. If he wants an average of 75, what score does he need in the fourth subject?

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

Solution

Let the fourth score be x. (60 + 70 + 80 + x) / 4 = 75. Solving gives x = 90.

Correct Answer: D — 85

Q. A student scores 80, 85, and 90 in three tests. What score does he need in the fourth test to have an average of 85?

A. 80
B. 85
C. 90
D. 95

Solution

Let the fourth score be x. (80 + 85 + 90 + x) / 4 = 85. Solving gives x = 95.

Correct Answer: C — 90

Q. A student scores 80, 90, and 70 in three subjects. If he wants an average of 85 after scoring in a fourth subject, what should he score?

A. 90
B. 95
C. 100
D. 85

Solution

Total score needed for average of 85 = 4 * 85 = 340. Current total = 80 + 90 + 70 = 240. Required score = 340 - 240 = 100.

Correct Answer: B — 95

Q. A student scores 80, 90, and 70 in three subjects. What score does he need in the fourth subject to achieve an average of 85?

A. 90
B. 95
C. 100
D. 85

Solution

Total score needed for average of 85 = 4 * 85 = 340. Current total = 80 + 90 + 70 = 240. Score needed = 340 - 240 = 100.

Correct Answer: B — 95

Q. A student scores 80, 90, and 70 in three subjects. What score does he need in the fourth subject to have an average of 85?

A. 90
B. 95
C. 100
D. 85

Solution

Let the score in the fourth subject be x. The average is (80 + 90 + 70 + x) / 4 = 85. Thus, 240 + x = 340, so x = 100.

Correct Answer: B — 95

Q. A sum of $12000 is due in 5 years. If the bankers discount is $3000, what is the rate of interest?

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

Solution

Bankers Discount = Principal - Present Value. Present Value = 12000 - 3000 = 9000. Rate = (3000 × 100) / (12000 × 5) = 5%.

Correct Answer: B — 6%

Q. A sum of $25000 is due in 2 years. If the bankers discount is $5000, what is the rate of interest?

A. 8%
B. 10%
C. 12%
D. 15%

Solution

Rate = (5000 × 100) / (25000 × 2) = 10%.

Correct Answer: B — 10%

Q. A sum of $3000 is invested at a compound interest rate of 7% per annum. What will be the amount after 5 years?

A. $4210.00
B. $4000.00
C. $4500.00
D. $4100.00

Solution

Total Amount = 3000(1 + 0.07)^5 = 3000(1.402552) = 4207.66

Correct Answer: A — $4210.00

Q. A sum of $3000 is invested at a compound interest rate of 7% per annum. What will be the total amount after 5 years?

A. $4200.00
B. $4205.00
C. $4210.00
D. $4215.00

Solution

Total Amount = 3000(1 + 0.07)^5 = 3000(1.402552) = 4207.66

Correct Answer: C — $4210.00

Q. A sum of $5000 is due in 2 years. What is the bankers discount at the rate of 10%?

A. $100
B. $200
C. $300
D. $400

Solution

Bankers Discount = (Principal × Rate × Time) / 100 = (5000 × 10 × 2) / 100 = $1000. The present value is $5000 / (1 + 0.10)^2 = $4132.23. Therefore, Bankers Discount = $5000 - $4132.23 = $867.77.

Correct Answer: B — $200

Q. A sum of money doubles itself in 10 years at compound interest. What is the rate of interest?

A. 7.2%
B. 10%
C. 5%
D. 12%

Solution

Using the Rule of 72, Rate = 72/10 = 7.2%

Correct Answer: A — 7.2%

Q. A sum of money doubles itself in 5 years at compound interest. What is the rate of interest?

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

Solution

Using the formula A = P(1 + r)^n, if A = 2P, then 2 = (1 + r)^5. Solving gives r = 0.10 or 10%.

Correct Answer: A — 10%

Q. A sum of money invested at compound interest grows to $5000 in 4 years at a rate of 6% per annum. What was the principal?

A. $4000
B. $4500
C. $3500
D. $3000

Solution

Let P be the principal. A = P(1 + r)^n; 5000 = P(1 + 0.06)^4; P = 5000 / 1.262476 = $3960.00.

Correct Answer: B — $4500

Q. A tank can be filled by a pipe in 10 hours and emptied by another pipe in 15 hours. If both pipes are opened together, how long will it take to fill the tank?

A. 5 hours
B. 6 hours
C. 10 hours
D. 12 hours

Solution

The net rate is 1/10 - 1/15 = 1/30. Therefore, it will take 30 hours to fill the tank.

Correct Answer: B — 6 hours

Q. A tank can be filled by a pipe in 10 hours and emptied by another pipe in 5 hours. If both pipes are opened together, how long will it take to fill the tank?

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

Solution

The net rate is 1/10 - 1/5 = -1/10. Therefore, the tank will never fill.

Correct Answer: C — 15 hours

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