2. 2IIM
Ascent Education’s
An IIM Alumni Venture
Question
In a 100m race, A can give B a start of 12 meters or 3 seconds. What is
the speed of B in m/sec and how long will A take to run 100m?
1.
3. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
3
In a 100m race, A can give B a start of 12 meters or 3 seconds. What is
the speed of B in m/sec and how long will A take to run 100m?
A can give B a start of 12 meters or 3 second start => B covers 12 meters
in 3 sec
So, speed of B = = 4 meters/sec
Time taken for B to complete the race = = 25 sec
Since A gives B a start of 3 sec, A completes the race 3 seconds before B.
Thus time taken by A to run 100 meters = 25 - 3 = 22 sec
1.
3
12
4
100
4. 2IIM
Ascent Education’s
An IIM Alumni Venture
Question
A can give B a start of 30 in a km race and A can give C a start of 50m in
a km race. How much start will B be able to give C in a km race?
2.
5. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
A can give B a start of 30m in a km race and A can give C a start of 50m
in a km race. How much start will B be able to give C in a km race?
A can give B start of 30 m or, when B travels 970 m, A can cover 1000 m.
A B C
1000 970 950
1000 ? = X
2.
B
A
970 m
1000 m
6. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
When A covers 1000 m, B covers 970, C covers 950. The Qn is when B
covers 1000 m, how much would C cover
X = =
Or the lead B should give
B = 1000 -
X = m = 20.61 m
970
950*1000
97
95000
97
95000
97
2000
7. 2IIM
Ascent Education’s
An IIM Alumni Venture
Question
A runs a 400m race at the speed of 8 m/sec. He gives B a start of 40m
and still beats him by 10 seconds. What is B's speed?
3.
8. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
A runs a 400m race at the speed of 8 m/sec. He gives B a start of 40m
and still beats him by 10 seconds. What is B's speed?
A takes 50 seconds.
B travels 360 m in 60 seconds.
Or, B travels @ 6 m/s.
3.
9. 2IIM
Ascent Education’s
An IIM Alumni Venture
Question
If A gives B a start of 20m in a race, A beats him by 10 seconds. On the
contrary, if A gives B a start of 40m, they finish the race in a dead heat. If
the length of the race is 400m, how long will A take to run the race?
4.
10. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
If A gives B a start of 20m in a race, A beats him by 10 seconds. On the
contrary, if A gives B a start of 40m, they finish the race in a dead heat. If
the length of the race is 400m, how long will A take to run the race?
A’s speed = A
B’s Speed = B
10B = 9A
4.
B
360
A
400
=
10
B
380
A
400
−=
10
B
360
B
380
=−
10
B
20
=
11. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
B = 2 m/s
B takes 180 seconds to run 360m.
A will take 180 seconds to run the race.
12. 2IIM
Ascent Education’s
An IIM Alumni Venture
Question
A and B start around a circular track of length 600m at speeds of 6m/s
and 9 m/sec from the same point, simultaneously and in the same
direction. When will they meet for the first time? How far from the
starting point will they meet, when they meet for the first time?
5.
13. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
A and B start around a circular track of length 600m at speeds of 6m/s
and 9 m/sec from the same point, simultaneously and in the same
direction. When will they meet for the first time? How far from the
starting point will they meet, when they meet for the first time?
Track length = 600 m
A’s speed = 6 m/s
B’s speed = 9 m/s
Rd speed = 3 m/s
Meet for the first time after - = 200 seconds.
In 200 s, A travels 200 x 6 = 1200 m.
So they meet @ the starting point.
5.
3
600
14. 2IIM
Ascent Education’s
An IIM Alumni Venture
Question
A and B run around a circular track at speeds of 8m/sec and 5m/sec
starting from the same point, simultaneously and in the same direction.
How many points with respect to the starting point on the circular track
will they meet, if the run at the above mentioned constant speeds
endlessly?
6.
15. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
A and B run around a circular track at speeds of 8m/sec and 5m/sec
starting from the same point, simultaneously and in the same direction.
How many points with respect to the starting point on the circular track
will they meet, if the run at the above mentioned constant speeds
endlessly?
Track length = T
A’s speed = 8 m/s
B’s speed = 5 m/s
Relative speed = 8 - 5 = 3 m/s
They meet after seconds.
Time taken for A to finish a lap =
6.
2
T
a
T
16. 2IIM
Ascent Education’s
An IIM Alumni Venture
Solution
Time taken for B to finish a lap =
Time after which they meet at the starting point
= LCM
=
No of positions = Time to meet @
= = 2.
b
T
b
T
a
T
,
1
T
b)(a,HCF
T
=
meet1forTime
pointStarting
st T/2
T/1
No of positions =
b)(a,HCF
b-a
