Q.1 A person walking takes 26 steps to come down on a escalator & it takes 30 sec for walking. Same person while running takes 18 sec. & 34 steps. How many steps are there ?

A) 46 steps

B) 47 steps

C) 48 steps

D) 49 steps

Ans. A

Let escalator moves at n steps/sec

Therefore,

26y+30n = 18n + 34 y

12n = 8

n= 2/3

Total no. of steps= 26+30*2/3 = 46 steps

Q.2 A man walks from P to Q at the rate of 5 km an hour & returns from Q to P at the rate of 3 km an hour. What is the rate in km per hour for the whole journey ?

A) 9/2

B) 47/9

C) 4

D) 15/4

Ans. D

L.C.M. of 3 & 5 = 15 km

Time taken in going from P to Q = 15/5 = 3

Time taken in coming from Q to P = 15/3 = 5

Therefore, total time in going & coming back = 5 + 3 = 8

Thus, average speed = 30 / 8 =15/ 4 km/hr

Q.3 A ship 40 km from shore springs a leak which admits 3 ¾ quintal of water in 12 min. 60 quintal would suffice to sink the ship. But its pumps can throw out 12 quintals of water in an hour. Find the average rate of sailing so that she may reach the shore just it begins to sink ?

A) 4.5 km/hr

B) 6 km/hr

C) 5 km/hr

D) 4 km/hr

Ans. A

In 12 min. leak admits = 15/4 quintals

In one hour leak admits = 15/4 * 60/12

=75/4 quintals

In one hour pumps throw out = 12 quintals

Water left in the ship in one hour = 75/4 – 12

=27/4 quintals

27/4 quintals of water is left in the ship in 1 hour

60 quintals of water is left in the ship in = 1*60*4 / 27 = 80/9

Now in 80/9hrs ship runs = 40 km

1 hr the ship runs = 40 * 9 / 80

=4.5 km

Q.4 Amit starts from a point A & walks to another point B, & then returns from B to A by his car & thus takes a total time of 6 hrs & 45 min. If he had driven both ways in his car, he would have taken 2hrs less. How long would it take for him to walk both the ways ?

A) 8hr 15min

B) 8h 45min

C) 7h 45min

D) 8h 30min

Ans. B

Let w be the time taken in one way by walking & c be the time taken in one way by car

Ist case

W+c=6h 45min

Or 2w +2c=13h 30min

IInd case

2c=4h 45min

From these two equations,we get

2w +2c=13h 30min

Or 2w+4h 45min=13h 30min

Or 2w=13h 30min – 4h 45min

Or 2w=8h 45min

Hence, if he walks both the ways time = 8h 45min

Q.5 Arya runs at a speed of 40 metres/min. Rahul follows him after an interval of 5 min. & runs at a speed of 50metres/min. Rahul’s dog runs at a speed of 60 metres/min & starts along with the Rahul. The dog reaches Aryans & then comes back to the Rahul, & continues to do so till Rahul reaches Aryan .What is the total distance covered by the dog ?

A) 980 meters

B) 750 meters

C) 600 meters

D) 1200 meters

Ans. D

Let they meet at a distance of y from start after time t of Rahul start

40*(5-t) = 50t

200 + 40t = 50t

T=200/10 = 20min.

Y=50*t= 50*20 = 1000 meters

Now see from the options except 1200 meters are smaller then 1000m & dog in any case has to move more than 1000m