Therefore,
,
Let A takes x hours to fill then B will take x-8 hr ,
20x-96=
-8x
-28x+96=0
x= 24 hr (because x cannot be 4 hr )
Example 8. If a car can finish a journey in 10 hr with a speed of 48 kmph . The by how
much the speed be increased to cover the same distance in 8 hr?
Solution:
Distance = speed
time = 48
10 = 480 km
To cover the same distance in 8 hr .
Speed = d/t = 480 / 8 = 60 kmph
Therefore, speed must be increased by 60-48 = 12 kmph .
Example 9. A man gets late by 2 hr if he walks ¾ th of his normal speed. What time will he
take to cover the same distance at his normal speed?
Solution:
let his normal speed be s kmph and normal time be t hr
Distance, d = st =
s
(t+2)
Or, 4t = 3t + 6 , t = 6 hr .
Example 10 . The speed of A and B are in ratio 4:5. A takes 40 min more than b to cover
the same distance. How much time does A take to cover this distance?
Solution.
Since the ratio of speed is 4 : 5 , so the ratio of time will be 5 : 4 .
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If it takes 40 min more , then
5x-4x = 40
x = 40 min
A takes 5 x min or 5
40 = 200 min.
Example 11. A man goes a hill at 20 kmph and comes down at 32 kmph along the same
path. What is his average speed?
Solution : Average speed =
Example12. A train travelling at the rate of 72 kmph crosses a pole in 8 seconds . What is
its length?
Solution: time = 8 secs
Speed = 72 kmph = 72
m/s = 20 m/s
Length = s
t = 8
20 = 160 m.
Example 13. A 200 m long train crossed a 700 m long platform in 1 in 6 seconds . What is
the speed of the train (in kmph ) ?
Solution :
Total length to be covered = length of the train + length of the platform
= 200+ 700 = 900
Tota time = 60+6 = 66 min
Speed = distance / time = 900/66 = 450/33 m/s =
kmph.
Example 14. If a boy walks from his house at 5 kmph , he reaches
school 5 min early , and
if he walks at 4 kmph he reaches 5 min late . How far does he work for his school?
Solution :
let his normal speed be x kmph .
Let his normal time t hr.
D = st
5 ( t -
)= 4 ( t +
)
5t -
= 4t +
t =
hr
Distance = 5 (
) = 41 km
Example 15. Two train travel in opposite direction one at 30 kmph and the other at 42
kmph. A man sitting in the slower train passes the faster train in 6 s. what is the length of
the faster train?
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CSAT Comprehensive
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CSAT Comprehensive
Solution :
since the train are running in opposite direction
, hence the length of the faster
train
= ( 30+42 )
6 m = 72
= 120 m
Example 16. A river runs at 3 kmph . if the time taken by a man to row his boat upstream
is twice the time taken by him to row it downstream , then at what speed can he row his
boat in still water ?
Solution :
let x be the speed of the boat in still water
and speed of the river = 3 kmph
Speed upstream = x- 3 kmph
Speed downstream = x+3 kmph
(x-3 )2t = ( x+ 3 ) t
2 ( x- 3) = x+ 3
X= 9 kmph.
Example 17. A train passes a pole in 20 s and crosses a platform of 200 m long in 60 s . find
the length of the train ?

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