Races and Games
Question
Q1.
In a km race x beats y by 20 meters or 5 seconds . Find the time taken by x to complete the race .
(a) 245 sec
(b) 250 sec
(c) 260 sec
(d) 230 sec
Solution. a
From the question , point is clear that y covers 20 meters in 5 seconds
So y's time to cover a km =
5/20
x 1000 = 250 sec
x will cover one km in( 250 - 5 sec) = 245 sec
Solution
Q2.
x is 2
2/3
times as fast as y . if x
gives y start of 30 meters , find the length of race course so that both of them reach at the same time ?
(a) 40 M
(b) 48 M
(c) 50 M
(d) 52 M
Solution. b
x's speed : y's speed = 2
2/3
: 1 =
8/3
: 1 = 8 : 3
Clearly in the race of 8 meter x will cover 5 meter therefore , he will cover 30 M in a race of
8/5
x 30 = 48 M
or
Short cut length of race course = lead
(
A's speed /A's speed - B's speed
)
= 30 x (
8/8 - 3
) = 30
(
8/5
) = 48 M
Solution
Q3.
A can run a race of one km in 2 min and B in 2 min 30 sec , By what distance can A beat B ?
(a) 150 M
(b) 100 M
(c) 200 M
(d) 250 M
Solution. c
As per question , to cover one km B will take 30 sec more than A .
So B will cover distance in 30 sec =
1000/150
x 30
= 200 M
∴ A beats B by 200 M
Solution
Q4.
In a 100 M run , A's speed is 6km/h . A gives B a start of 6 meters and still beats him by 6 seconds . Find the speed of B .
(a) 5.12 km/h
(b) 5 km/h
(c) 4 km/h
(d) 13.28 km/h
Solution. a
A's time to cover 100 M =
=
100 x 18/30
= 60 sec
= B will cover 94 M in 66 sec
∴ B's speed =
94/66
x
18/5
=
1692/330
= 5.12 km/h
Solution
Q5.
In a run of 200 M , A runs 10 km/h . A gives B a start of 20 M and still beats him by 10 sec . Find the speed of B .
(a) 6.4 km/h
(b) 7.902 km/h
(c) 8 km/h
(d) 10 km/h
Solution.
A's time to cover 200 M =
=
200 x 18/50
= 72 sec
Now , B will cover 180 M 82 sec
So B's speed =
180/82
x
18/5
= 7.902 km/h
Solution
