1. Two motor cars start from one point and move along two roads at right angles to each other. If their speeds be respectively 36 k m/hr and 48 km/hr, then after half and hour they will be x km apart. What is x?"

A. 30 km B. 40 km C. 12 km D. 84 km

Answer: Option A
Explanation: [latex] {x}^{2}[/latex] = [latex] {24}^{2}[/latex] + [latex] {18}^{2}[/latex]
= 576 + 324 = 900
i.e, x = [latex]\sqrt {900}[/latex] = 30 km
2. A man goes from Delhi to Dehradun. Half the distance he covers by bus at an average speed of 50 km/hr and the other half by train at an average speed of 70 km/hr. The average speed for the whole journey was

A. 56 km/hr B. 64 km/hr C. 60 km/hr D. None of these

Answer: Option D
Explanation:
v - bar = [latex]\frac {2uv} {u + v}[/latex] = [latex]\frac {2 * 50 * 70} {50 + 70}[/latex] =[latex] 58 \frac {1} {3}[/latex]
3. A man covers a distance of 100 km partly by bus at 40 km/hr and partly by scooter at 30 km/hr. His average speed for the whole journey was 32 km/hr. How far did he go by bus?

A. 20 km B. 25 km C. 30 km D. 40 km

Answer: Option B
Explanation:
[latex]\frac {x km (100 - x) km} {@ 40kph @ 30 lph}[/latex]
Average speed = [latex]\frac {Total distance} {Total time}[/latex]
i.e, 32 = [latex]\frac {100} {\frac {x}{40} - \frac {100 - x}{30}}[/latex]
x = 25 km
4. A person shooting at a target from a distance of 450 metres finds that the sound of the bullet hitting the target comes [latex]\frac {1} {2}[/latex] seconds after he fired. A person equidistant from the target and shooting point hears the bullet hit 3 seconds after he heard the gun. The speed of sound is

A. 300 m/s B. 350 m/s C. 250 m/s D. 400 m/s

Answer: Option A
Explanation:
v - bar = [latex]\frac {450m} {1s\frac{1}{2}}[/latex] = 300 m/s
5. A monkey climbs a slippery pole 12 m high. It rises 1 meter in every one minute and slip [latex]\frac {1} {2}[/latex] meter in every next minute. Find how soon it will reach the top?

A. 45 min B. 40 min C. 35 min D. 48 min

Answer: Option A
Explanation:
Average speed = 1 meter/ 4 minutes
For 11 m, time taken = 44 minutes
For last 1 m, jump add 1 minutes
i.e, Time taken = 45 minutes

6. A boy walks at 4 km/hr. and reaches his school 5 minutes late. Next day he walks at 5 km/hr and start at the same time, reaches his school 10 minutes. early. How far is the school from his house?

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

Answer: Option B
Explanation:
[latex]\frac {d} {4} - \frac {d}{5}[/latex] [latex]\frac {15} {60}[/latex]
[latex]\frac {5d - 4d} {20}[/latex] = [latex]\frac {15} {60}[/latex]
[latex]\frac {d} {20}[/latex] = [latex]\frac {1} {4}[/latex]
d = 5 km
7. A train starts from Delhi with a certain number of passengers. At Ghaziabad 110 get down and 100 get in. At Aligrah 50% get down and 25 get in. At Kanpur 5 half of them get down and 50 get in. When t he t r ai n leaves Kanpur there are 200 passengers. How many did board the train at Delhi?

A. 300 B. 400 C. 500 D. 600

Answer: Option C
Explanation:
Let there were n passengers at Delhi.
n = Delhi, [latex]\frac {n} {10} + 10 [/latex] = Ghaziabad, [latex]\frac {n} {20} + 50 + 25 [/latex] = Aligarh, [latex]\frac {n} {40} + \frac {75} {2} + 50 [/latex] = Kanpur (200)
[latex]\frac {n} {40} + \frac {75} {2} + 50 [/latex] = 200
n = 500
8. The radius of a circular wheel is 35 cm and it moves at the rate of 500 revolutions per minute. The speed of wheel is

A. 50 km/hr B. 60 km/hr C. 63 km/hr D. 66 km/hr

Answer: Option D
Explanation:
Speed = 500 rpm
= 500 * 2 * [latex]\frac {22} {7}[/latex] * [latex]\frac {35} {100}[/latex] * 60 * [latex]\frac {1} {100}
[/latex] = 66 km/hr
9. Diameter of the front wheel and hind wheel of a van are 70 cm and 98 cm respectively. How many more revolutions the front wheel will make when the hind wheel in going over a distance of 154 kms?

A. 10,000 B. 15,000 C. 20,000 D. 25,000

Answer: Option C
Explanation:
[latex] {n}_{1} {c}_{1}[/latex] = 154 km
i.e, [latex]{n}_{1}[/latex] * [latex]\frac {22} {7}[/latex] * 70 cm = 15400000 cm
[latex]{n}_{1}[/latex] = 70000
and [latex] {n}_{1} {c}_{2}[/latex] = 154 km
i.e, [latex]{n}_{2}[/latex] * [latex]\frac {22} {7}[/latex] * 98 cm = 15400000 cm
[latex]{n}_{2}[/latex] = 50000
i.e, [latex] {n}_{1} - {n}_{2}[/latex] = 20000 cm
10. Two men X and Y start from a place P, walking at 3 km/hr, and 4 km/hr. By how much distance apart they will be after 4 hours if they are walking in the same direction?

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

Answer: Option A
Explanation:
d = v * t = (4 – 3) * 4 = 4 km

11. In the above question, what will be the distance between them after 5 hours if they walk in opposite directions?

A. 35 km B. 14 km C. 21 km D. 28 km

Answer: Option A
Explanation:
d = (4 + 3) * 5 = 35 km
12. A person has to make a journey of 72 km. He rides a cycle at 12 kms/hr. After going certain distance, the cycle got punctured and he walks the remaining distance at [latex] 4 \frac {1} {2}[/latex] km/hr. Where did the cycle got punctured if total time taken for the journey was [latex] 8 \frac {1} {2}[/latex] hours?

A. 18 km B. 54 km C. 36 km D. 48 km

Answer: Option B
Explanation:
[latex] 8 \frac {1} {2}[/latex] = [latex]\frac {x} {12}[/latex] + [latex]\frac {72 - x} {4 \frac {1}{2}}[/latex]
x = 54 km
13. A car is stolen at 4.00 a.m the thief drives it towards north at a speed of 50 k m/hr. The theft is discovered at 4.30 a.m. and a police jeep is set towards north at 60 kms/hr. At what time did the jeep will overtake the car?

A. 6.00 a.m. B. 7.00 a.m. C. 7.30 a.m. D. 6.30 a.m.

Answer: Option B
Explanation:
[latex] \frac {d} {50} - \frac {d} {60}[/latex] = [latex] \frac {1} {2}[/latex]
[latex] \frac {d} {300}[/latex] = [latex] \frac {1} {2}[/latex]
d = 150
i.e, t = [latex] \frac {150} {50}[/latex] = 3 hrs
Hence jeep will overtake the car at 7.00 a.m.
14. A student goes to his school from his house walking at 4 km/hr. and reaches his school 10 min. late Next day starting at same the time he walks at 6 km/ hr and reaches his school 15 minutes early. How far is the school from the house?

A. 3 km B. 5 km C. 9 km D. 24 km

Answer: Option B
Explanation:
[latex] \frac {d} {4} - \frac {d} {6}[/latex] = [latex] \frac {25} {60}[/latex]
[latex] \frac {3d - 2d} {12}[/latex] = [latex] \frac {5} {12}[/latex]
d = 5 km
15. A train traveled from A to B and back in a certain time at the rate of 60 km/hr. But if the train had traveled from A to B at the rate of 80 km/hr. and back from B to A at the rate of 40 km/hr it would take two hour longer. The distance bet ween A and B is

A. 480 km B. 320 km C. 540 km D. 180 km

Answer - Option A
Explanation -
[latex] \frac {d} {80} - \frac {d} {40}[/latex] = [latex] \frac {d} {60} + \frac {d} {60}[/latex] = 2
[latex] \frac {3d + 6d -4d -4d} {240} [/latex] 2
[latex] \frac {d} {240}[/latex] = 2
d = 480