Q1. Given below are two statements :
Statement I : Ravi walks from his house at a speed of 5 km per hour and reaches the college 10 minutes late. If he increases the speed by 1 km per hour next day, he reaches the college 4 minutes earlier than the scheduled time. If the college is P km far from his house, then P = 7.5 km.
Statement II: Amit runs 2 1/3 times as fast as Babita. If Amit gives Babita a start of 80 meters, then the winning post must be 140 meters far so that Amit and Babita might reach it at the same time.
In the light of the above statements, choose the correct answer from the options given below.
A Both Statement I and Statement II are true
B Both Statement I and Statement II are false
C Statement I is true but Statement II is false
D Statement I is false but Statement II is true
EXPLANATION
.D
Statement I:
Let the actual time taken by Ravi to reach the college be ‘t’.
If Ravi travels at a speed of 5 km/hr, time taken is t + 10/60
If Ravi travels at a speed of 6 km/hr, time taken is t – 4/60
Distance = speed*time = P = 5(t + 10/60) = 6(t – 4/60)
5(t + 10/60) = 6(t – 4/60)
5t + 50/60 = 6t − 24/60
t = 74/60
Distance(P) = 5 (74/60 + 10/60) = 5 (84/60) = 7 km
Therefore, statement I is incorrect.
Statement II:
Let the speed of Babita be 3x.
Therefore, statement II is correct.
The answer is option D.
Q2. A train running at 18 km per hour crosses a mark on the platform in 9 seconds and takes 25 seconds to cross the platform. If P is the length of the train and Q is the length of the platform in meters, then (P, Q) = _ .
A (45, 80)
B (45, 75)
C (50, 90)
D (50, 80)
EXPLANATION
A
Speed of train = 18 km/hr = 5 m/s
Let the length of train be ‘P’
It is given,
P / 5 = 9
P = 45m
Let the length of platform be ‘Q
It is given,
P + Q / 5 = 25
P+Q = 125
Q = 125 – 45 = 80m
(P, Q) = (45, 80)
The answer is option A.
Leave a Reply