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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:
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
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:
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?
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
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?
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:
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?
Total number of votes polled = (1136 + 7636 + 11628) = 20400.
Required percentage = (11628 / 20400 x 100) % = 57%.