All Free Mathematics MCQs with Answers

• A. 140m
• B. 125m
• C. 100m
• D. 110m

Explanation: Their speeds are in the ratio X:Y = 48:42 = 8:7. When X runs 1,000 m, Y runs 1,000 × 7/8 = 875 m, so X beats Y by 1,000 - 875 = 125 m.

• A. 86 sec
• B. 80 sec
• C. 76 sec
• D. None of these

Explanation: When A completes 300 m, B has completed 277.5 m, so their speed ratio is A:B = 300:277.5 = 40:37.

• A. 50
• B. 40
• C. 25
• D. 15

Explanation: A can give B 20 points in a game of 60, so A:B = 60:40 = 3:2. A can give C 30 points, so A:C = 60:30 = 2:1; hence B:C = 4:3.

• A. 57.5 m
• B. 127.5 m
• C. 150.7 m
• D. 98.6 m

Explanation: A beats B by 100 m in 1,000 m, so A:B = 1,000:900 = 10:9. B beats C by 100 m in 800 m, so B:C = 800:700 = 8:7; therefore A:C = 80:63.

• A. 150 m
• B. 125 m
• C. 130 m
• D. 100 m

Explanation: A's speed is 1,000 m ÷ 4.5 min, while B's speed is 1,000 m ÷ 5 min. In 4.5 minutes, B covers (1,000 ÷ 5) × 4.5 = 900 m, so A can give B…

• A. 200 sec
• B. 190 sec
• C. 210 sec
• D. 150 sec

Explanation: When A runs 1,000 m, B runs 950 m, so their speed ratio is A:B = 1,000:950 = 20:19.

• A. 111.12 m
• B. 888.88 m
• C. 777.52 m
• D. 756.34 m

Explanation: A giving B a 100 m start gives A:B = 1,000:900 = 10:9, while A giving C a 200 m start gives A:C = 1,000:800 = 5:4.

• A. 19
• B. 28
• C. 30
• D. 37

Explanation: The elevators close a distance of 51 - 11 = 40 floors at a combined rate of 57 + 63 = 120 floors per minute, so their meeting time is…

• A. 5000 m/hr
• B. 5200m/hr
• C. 5400 m/hr
• D. 5600 m/hr

Explanation: The tank must receive 225 m × 162 m × 0.2 m = 7290 m3 of water in 5 h, so the flow rate is 7290 m3 ÷ 5 h = 1458 m3/h.

• A. 26hours
• B. 42hours
• C. 52hours
• D. 65hours

Explanation: The reservoir volume to be filled is 80 m × 60 m × 6.5 m = 31,200 m3. The pipe area is (0.2 m)2 = 0.04 m2, and water speed is 15 km/h =…

• A. 11 hours
• B. 12 hours
• C. 220 hours
• D. 22 hours

Explanation: To return to the starting point, each traveller must cover a whole number of 11 km laps.

• A. 5 min
• B. 5.5 min
• C. 5.2 min
• D. None

Explanation: The bells meet again after the least common multiple of their intervals.

• A. 36km/h
• B. 45km/h
• C. 48km/h
• D. 50km/h

Explanation: For equal distances, average speed is total distance divided by total time, or 2uv/(u+v).

• A. Geo means Earth
• B. Metron means Measurement.
• C. Hence Geomatery means
• D. Earth measurement

Explanation: The word geometry comes from the Greek words geo, meaning Earth, and metron, meaning measurement.

• A. (0,1)
• B. (1,1)
• C. (0,0)
• D. (1,0)

Explanation: The origin is the point where the x-axis and y-axis intersect, and both coordinates are zero. Therefore, its coordinates are (0,0).

• A. 5 metres
• B. 8 metres
• C. 10 metres
• D. 12 metres

Explanation: Let the horizontal distance be d metres. From the bottom of the pole, tan 60° = 15 metres ÷ d, so d = 5√3 metres; the 30° angle from the…

• A. 30°
• B. 45°
• C. 60°
• D. 90°

Explanation: For the right triangle, tan θ = height ÷ shadow length. Since the shadow is √3 times the height, tan θ = height ÷ (√3 x height) = 1/√3…

• A. 149 m
• B. 156 m
• C. 173 m
• D. 200 m

Explanation: Using tan 30° = height/distance, the distance is 100 m ÷ tan 30° = 100 m ÷ 0.577 ≈ 173 m.

• A. 50°
• B. 60°
• C. 70°
• D. 80°

Explanation: For the right triangle, tan θ = opposite/adjacent = 2√3 m ÷ 2 m = √3, and tan 60° = √3, so θ = 60°.

• A. 173 m
• B. 200 m
• C. 273 m
• D. 300 m

Explanation: The ships are on opposite sides, so their distances from the lighthouse foot are added: 100 m ÷ tan 30° ≈ 173 m and 100 m ÷ tan 45° = 100…