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1.A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

A45 m

B.50 m-Answer

C54 m

D72 m

2 kmph = ( 2 x5 /18)m/sec = 5 /9m/sec.

4 kmph = ( 4 x 518)m/sec = 10 /9m/sec.

Let the length of the train be x metres and its speed by y m/sec.

Then, (x /y-5/9) = 9 and (x/y-10/9 )= 10.

9y-5=xand 10 (9y-10)=9x

9y-x=5 and 90y-9x=100

on solving we get x=50

Length of the train is 50 m

2.A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:

A.1 km/hr -Answer

B.1.5 km/hr

C. 2 km/hr

D. 2.5 km/hr

Suppose he move 4 km downstream in x hours. Then,

Speed downstream =(4/x)km/hr

Speed up stream =(3/x)km/hr

48/4/x+48(3/x)=14 or x=1/2

So,speed downstream = 8 km/hr,speed upstream =6km/hr

Rate of the stream = 1/2(8-6)km/hr =1 km/hr.

3.A pupil’s marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:

A.10

B20

C. 40-Answer

D. 73

Let there be x pupils in the class.

Total increase in marks =(x*1/2)=x/2

Therefore x/2=(83-63) =x/2=20 =x=40

4 A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

A. 3/4

B4/7-Answer

C.1/8

D.3/7.

Let number of balls = (6 + 8) = 14.

Number of white balls = 8.

P (drawing a white ball) = 8 /14 = 4 /7 .

5.The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

A. 3 : 3 : 10

B. 10 : 11 : 20

C. 23 : 33 : 60-Ans

D. Cannot be determined

Explanation:

Let A = 2k, B = 3k and C = 5k.

A’s new salary = 115/100 of 2k =115/100 x 2k = 23k/10

B’s new salary = 110 /100 of 3k = 110 /100 x 3k = 33k/10

C’s new salary = 120 of 5k = 120 x 5k = 6k

New ratio 23k /10: 33k/10 : 6k = 23 : 33 : 60

6.There were two rooms of students room A and room B.If 10 students from room A are transferred to room B then the no of students in both the room will be equal .If 20 students from room B are transferred to room A then the no. of students in room A will be double the no of students in room A.Then what are the no. of students in room A?

7.The time taken by boat to travel 4 meters dowmstream is 4 hours 48 min and that the upstream 4 hours .Find the speed of the boat in still water and the speed of the stream.

8.An accurate clock shows 8 o’clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon?

A. 144º

B150º

C.168º

D180º

Explanation:

Angle traced by the hour hand in 6 hours = (360/12) x 6 º = 180º.

9.If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:

A50 km-Ans

B.56 km

C. 70 km

D. 80 km

Let the actual distance travelled be x km.

Thenx = x/10 + 20/14

14x = 10x + 200 4x = 200

x = 50 km.

10 Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?

A. 57%

B. 60%

C. 65%

D. 90%

Total number of votes polled = (1136 + 7636 + 11628) = 20400.

Required percentage = (11628 / 20400 x 100) % = 57%.