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QUESTION: 1

Two pipes A and B can independently fill a tank completely in 20 and 30 minutes respectively. If both the pipes are opened simultaneously, how much time will they take to fill the tank completely?

[2015]

Solution:

Time taken by both tanks

QUESTION: 2

Two cities A and B are 360 km apart. A car goes from A to B with a speed of 40 km/hr and returns to A with a speed of 60 km/hr. What is the average speed of the car?

[2015]

Solution:

Average speed of two cars at a speed V_{1} and V_{2} km/hr

= 48 km/hr

QUESTION: 3

In a 500 metres race, B starts 45 metres ahead of A, but A wins the race while B is still 35 metres behind. What is the ratio of the speeds of A to B assuming that both start at the same time?

[2015]

Solution:

Total distance = 500m

Distance covered by A = 500m

Distance covered by B = 500 – 45 – 35

= 500 – 80

= 420

QUESTION: 4

A worker reaches his factory 3 minutes late if his speed from his house to the factory is 5 km/hr, if he walks at a speed of 6 km/hr then he reaches the factory 7 minutes early. The distance of the factory from his house is

[2015]

Solution:

Let the distance is x km

ATQ,

∴ x = 5 km

QUESTION: 5

A and B decide to travel from place X to place Y by bus. A has ₹ 10 with him and he finds that it is 80% of the bus fare for two persons. B finds that he has ₹ 3 with him and hands it over to A. In this context, which one of the following statements is correct?

[2014]

Solution:

Let cost of 1 ticket is ₹ x.

Now B gives ₹ 3 to A.

So, A has 13 ₹.

Cost of 2 tickets = ₹ 12.50, which is more than enough to buy 2 tickets.

∴ (a) Rules out

(b) is clearly ruled out

(c) is true, because after buying 2 tickets.

A is left with ₹ 13 – 12.50 = 50 paise

QUESTION: 6

A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the second point and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points?

[2014]

Solution:

∴ 1 + 2 + 3 + ........ n = 36

n(n + 1) = 72

⇒ n = 8

∴ Leaving the end points the no. of points starting from A is 7.

Similarly starting from B, the no. of points will be 7. And also no. of the points between A & B will coincide.

∴ Total no. of points

= 7 + 7 = 14

QUESTION: 7

Two cars start towards each other, from two places A and B which are at a distance of 160 km. They start at the same time 08 :10 AM. If the speeds of the cars are 50 km and 30 km per hour respectively, they will meet each other at

[2014]

Solution:

Suppose the cars meet at point C after ‘t’ hrs.

∴ AC = 50 t and BC = 30 t

∴ 50 t + 30 t = 160

So, the cars will meet at 10 : 10 AM

QUESTION: 8

Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C is

[2014]

Solution:

QUESTION: 9

A train travels at a certain average speed for a distance of 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete the total journey, what is the original speed of the train in km/hr?

[2013]

Solution:

Let the original speed = x

Total time taken = 3 hr

⇒ (x) (x + 6) = 21(x + 6) + 24(x)

⇒ x^{2} – 39x – 126 = 0

⇒ x^{2} – 42x + 3x = 126 = 0

⇒ (x – 42) (x + 3) = 0

x = 42, x = – 3

x = – 3 is rejected.

Hence, original speed was 42 km/hr.

QUESTION: 10

A thief running at 8 km/hr is chased by a policeman whose speed is 10 km/hr. If the thief is 100 m ahead of the policeman, then the time required for the policeman to catch the thief will be

[2013]

Solution:

If we consider the difference of speeds, policeman is 2 km/hr leading speed and he can catch the thief at 100 m ahead by

QUESTION: 11

Four cars are hired at the rate of ₹ 6 per km plus the cost of diesel at ₹ 40 a litre. In this context, consider the details given in the following table:

Which car maintained the maximum average speed?

[2013]

Solution:

Let the distances travelled by cars A, B, C and D be a, b, c and d respectively.

Then, the total payment for car A

Hence, average speed of ‘A’

For B, total payment for car B

⇒ 10b = 1950

∴ b = 195

Hence, average speed of ‘B’ = b/25

For C, total payment for car C

Hence averge speed by ‘C’ = c/24

For D, total payment for car D

Hence, the average speed of

All speeds except A are less than 9. Hence it’s greatest value.

QUESTION: 12

A person can walk a certain distance and drive back in six hours. He can also walk both ways in 10 hours. How much time will he take to drive both ways?

[2013]

Solution:

2-way walk = 10 hrs

∴ 1-way walk = 5 hrs

1-way walk + 1 way drive = 6 hrs

∴ 1 way drive = 6 – 5 = 1 hr

Hence, two way drive take 2 hrs.

QUESTION: 13

Mr. Kumar drives to work at an average speed of 48 km per hour. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. How far is his office?

[2012]

Solution:

∴ d = 40 km

QUESTION: 14

If a bus travels 160 km in 4 hours and a train travels 320 km in 5 hours at uniform speeds, then what is the ratio of the distances travelled by them in one hour?

[2011]

Solution:

Distance covered by a bus in 4 hours = 160 km.

∴ Distance covered by a bus in 1 hour = 160/4 = 40 km

Further, Distance covered by a train in 5 hours = 320 km

∴ Distance covered by a train in 1 hour = 320/5 = 64km

Required ratio = 40/64 = 5/8 = 5:8

QUESTION: 15

Three men start together to travel the same way around a circular track of 11 km. Their speeds are 4, 5.5 and 8 kmph respectively. When will they meet at the starting point for the first time?

[2010]

Solution:

Let the minimum time be t, when they meet at the starting point for the first time. So, the net distance covered must be a multiple of 11.

Now, (4 + 5.5 + 8) t = 11 (n)

where, n is an integer.

minium value of n is 35, so that we can get an appropriate value of time.

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