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UPSC CDS 2 2018 Math Paper
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© examsnet.com
Question : 30
Total: 100
In a race of 1000 m, A beats B by 150 m, while in another race of 3000 m, C beats D by 400 m. Speed of B is equal to that of D. (Assume that A, B, C and D run with uniform speed in all the events). If A and C participate in a race of 6000 m, then which one of the following is correct ?
[2018 CDS-II]
A beats C by 250 m
C beats A by 250 m
A beats C by 115.38 m
C beats A by 115.38 m
Validate
Solution:
S
A
S
B
=
1000
1000
−
150
=
1000
850
=
20
17
∴ Let
S
A
=
20
x
then
S
B
=
17
x
S
C
S
D
=
3000
3000
−
400
=
3000
2600
=
15
13
∴ Let
S
C
=
15
y
then
S
D
=
13
y
Since
S
B
=
S
D
,
therefore,
17
x
=
13
y
⇒
y
=
17
13
x
Now
S
c
=
15
×
17
13
×
S
A
S
C
=
20
x
15
×
17
13
x
=
20
×
13
15
×
17
=
52
51
Distance by which A beats C in6000 m race
=
(
52
−
51
)
52
×
6000
=
115.38
m
© examsnet.com
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