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. Two pipes can fill a tank in 10 hours and 15 hours respectively. If the first pipe is opened for 5 hours and then the second pipe is opened, how long will it take to fill the tank?

A. 3 hours
B. 4 hours
C. 5 hours
D. 6 hours

Solution

The first pipe fills 1/2 of the tank in 5 hours. The remaining half can be filled by both pipes in 2 hours.

Correct Answer: B — 4 hours

Q. Two pipes can fill a tank in 8 hours and 12 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

A. 4.8 hours
B. 5 hours
C. 6 hours
D. 7 hours

Solution

The combined rate is 1/8 + 1/12 = 5/24. Therefore, time taken = 24/5 = 4.8 hours.

Correct Answer: A — 4.8 hours

Q. Two pipes can fill a tank in 9 hours and 12 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

A. 4.5 hours
B. 5 hours
C. 6 hours
D. 7 hours

Solution

The combined rate is 1/9 + 1/12 = 7/36. Therefore, it will take 36/7 = 5.14 hours to fill the tank.

Correct Answer: C — 6 hours

Q. What day of the week was July 4, 1776?

A. Monday
B. Tuesday
C. Wednesday
D. Thursday

Solution

Using Zeller's Congruence, July 4, 1776 falls on a Thursday.

Correct Answer: C — Wednesday

Q. What day of the week will it be on December 31, 2023 if January 1, 2023 is a Sunday?

A. Saturday
B. Sunday
C. Monday
D. Tuesday

Solution

2023 has 365 days, which is 52 weeks and 1 day. December 31, 2023 will be one day before January 1, 2024, which is a Sunday, making it Saturday.

Correct Answer: A — Saturday

Q. What day of the week will it be on December 31, 2025 if January 1, 2025 is a Wednesday?

A. Friday
B. Saturday
C. Sunday
D. Monday

Solution

2025 is not a leap year, so it has 365 days. From January 1 to December 31 is 364 days, which is 52 weeks + 0 days. Therefore, December 31, 2025 will also be a Wednesday.

Correct Answer: B — Saturday

Q. What is 0.75 as a fraction?

A. 1/2
B. 3/4
C. 2/3
D. 1/4

Solution

0.75 = 75/100 = 3/4 after simplification.

Correct Answer: B — 3/4

Q. What is 0.9 as a fraction?

A. 9/10
B. 1/10
C. 1/5
D. 1/2

Solution

0.9 = 9/10.

Correct Answer: A — 9/10

Q. What is 15% of 200?

A. 25
B. 30
C. 35
D. 40

Solution

15% of 200 is calculated as (15/100) * 200 = 30.

Correct Answer: B — 30

Q. What is 25% of 200?

A. 25
B. 50
C. 75
D. 100

Solution

25% of 200 is calculated as (25/100) * 200 = 50.

Correct Answer: B — 50

Q. What is the area of a circle with a diameter of 10 cm? (Use π = 3.14)

A. 78.5 cm²
B. 31.4 cm²
C. 50 cm²
D. 100 cm²

Solution

Radius = diameter/2 = 10 cm/2 = 5 cm. Area = π × radius² = 3.14 × (5 cm)² = 78.5 cm².

Correct Answer: A — 78.5 cm²

Q. What is the area of a rectangle with a length of 10 cm and a width of 5 cm?

A. 50 cm²
B. 40 cm²
C. 30 cm²
D. 60 cm²

Solution

Area = length × width = 10 cm × 5 cm = 50 cm².

Correct Answer: A — 50 cm²

Q. What is the area of a rectangle with a length of 8 cm and a width of 5 cm?

A. 30 cm²
B. 40 cm²
C. 50 cm²
D. 60 cm²

Solution

Area = length × width = 8 cm × 5 cm = 40 cm².

Correct Answer: B — 40 cm²

Q. What is the area of a rectangle with length 10 cm and width 5 cm?

A. 50 cm²
B. 15 cm²
C. 25 cm²
D. 30 cm²

Solution

Area = length × width = 10 cm × 5 cm = 50 cm².

Correct Answer: A — 50 cm²

Q. What is the area of a regular hexagon with a side length of 3 m?

A. 15.59 m²
B. 18.00 m²
C. 23.38 m²
D. 27.00 m²

Solution

Area = (3√3/2) × side² = (3√3/2) × (3 m)² ≈ 15.59 m².

Correct Answer: A — 15.59 m²

Q. What is the area of a rhombus with diagonals of 10 cm and 6 cm?

A. 30 cm²
B. 40 cm²
C. 20 cm²
D. 50 cm²

Solution

Area = 1/2 × diagonal1 × diagonal2 = 1/2 × 10 cm × 6 cm = 30 cm².

Correct Answer: A — 30 cm²

Q. What is the area of a rhombus with diagonals of 10 cm and 8 cm?

A. 40 cm²
B. 45 cm²
C. 50 cm²
D. 55 cm²

Solution

Area = 1/2 × d1 × d2 = 1/2 × 10 cm × 8 cm = 40 cm².

Correct Answer: A — 40 cm²

Q. What is the area of a rhombus with diagonals of lengths 10 cm and 24 cm?

A. 120 cm²
B. 60 cm²
C. 80 cm²
D. 100 cm²

Solution

Area = (d1 × d2) / 2 = (10 cm × 24 cm) / 2 = 120 cm².

Correct Answer: A — 120 cm²

Q. What is the area of a sector of a circle with a radius of 10 cm and a central angle of 60 degrees (use π ≈ 3.14)?

A. 17.45 cm²
B. 20.93 cm²
C. 15.71 cm²
D. 25.13 cm²

Solution

Area = (θ/360) × π × radius² = (60/360) × 3.14 × (10 cm)² = 17.45 cm².

Correct Answer: A — 17.45 cm²

Q. What is the area of a sector of a circle with a radius of 10 cm and an angle of 60 degrees? (Use π = 3.14)

A. 17.5 cm²
B. 15.7 cm²
C. 20.9 cm²
D. 25.0 cm²

Solution

Area = (θ/360) × π × r² = (60/360) × 3.14 × (10 cm)² = 17.5 cm².

Correct Answer: A — 17.5 cm²

Q. What is the area of a sector of a circle with a radius of 4 m and a central angle of 90 degrees?

A. 6.28 m²
B. 12.56 m²
C. 3.14 m²
D. 9.42 m²

Solution

Area of sector = (θ/360) × πr² = (90/360) × π × (4 m)² = (1/4) × 3.14 × 16 m² = 12.56 m².

Correct Answer: B — 12.56 m²

Q. What is the area of a sector of a circle with a radius of 4 m and a central angle of 90 degrees? (Use π = 3.14)

A. 12.56 m²
B. 6.28 m²
C. 3.14 m²
D. 9.42 m²

Solution

Area of sector = (θ/360) × πr² = (90/360) × 3.14 × (4 m)² = 12.56 m² / 4 = 3.14 m².

Correct Answer: B — 6.28 m²

Q. What is the area of a sector of a circle with a radius of 5 cm and a central angle of 60 degrees? (Use π = 3.14)

A. 13.09 cm²
B. 15.71 cm²
C. 10.42 cm²
D. 12.27 cm²

Solution

Area of sector = (θ/360) × πr² = (60/360) × 3.14 × (5 cm)² = 13.09 cm².

Correct Answer: A — 13.09 cm²

Q. What is the area of a sector of a circle with a radius of 6 cm and a central angle of 60 degrees? (Use π = 3.14)

A. 18.84 cm²
B. 12.56 cm²
C. 9.42 cm²
D. 6.28 cm²

Solution

Area = (θ/360) × π × r² = (60/360) × 3.14 × (6 cm)² = 18.84 cm².

Correct Answer: A — 18.84 cm²

Q. What is the area of a square with a side length of 4 m?

A. 8 m²
B. 12 m²
C. 16 m²
D. 20 m²

Solution

Area = side × side = 4 m × 4 m = 16 m².

Correct Answer: C — 16 m²

Q. What is the area of a trapezoid with bases of 10 m and 6 m, and a height of 4 m?

A. 40 m²
B. 32 m²
C. 24 m²
D. 36 m²

Solution

Area = 1/2 × (base1 + base2) × height = 1/2 × (10 m + 6 m) × 4 m = 32 m².

Correct Answer: B — 32 m²

Q. What is the average of the first five prime numbers?

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

Solution

The first five prime numbers are 2, 3, 5, 7, 11. Average = (2 + 3 + 5 + 7 + 11) / 5 = 28 / 5 = 5.6.

Correct Answer: C — 7

Q. What is the average of the numbers 10, 20, and 30?

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

Solution

The average is (10 + 20 + 30) / 3 = 60 / 3 = 20.

Correct Answer: B — 20

Q. What is the Banker's Discount on a bill of $2500 due in 9 months at a rate of 8%?

A. $150
B. $120
C. $100
D. $180

Solution

Banker's Discount = (2500 x 8 x 9/12) / 100 = $150

Correct Answer: A — $150

Q. What is the Banker's Discount on a bill of $500 due in 3 months at a rate of 6% per annum?

A. $7.50
B. $8.00
C. $9.00
D. $10.00

Solution

Banker's Discount = (Principal x Rate x Time) / 100 = (500 x 6 x 3/12) / 100 = $7.50

Correct Answer: A — $7.50

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