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UPSC 2015 CDS II Math Paper
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© examsnet.com
Question : 24
Total: 100
In a race A, B and C take part. A beats B by 30 m, B beats C by 20 m and A beats C by 48 m. Which of the following is/are correct ?
1. The length of the race is 300 m.
2. The speeds of A, B and C are in the ratio 50 : 45 : 42.
Select the correct answer using the code given below:
[2015 CDS-II]
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Validate
Solution:
Let the length of the race be x m and A reaches the finish line after T seconds.
Therefore, Speed of
A
=
v
A
=
x
T
m/s
Speed of B
=
v
B
=
x
−
30
T
m/sx
Speed of C
=
v
C
=
x
48
T
m/s
Suppose B reaches the finish line after t seconds.
Speed of B
=
v
B
=
x
t
m/s
Speed of C
=
v
C
=
x
−
20
t
m/s
∴
v
B
v
C
=
x
−
30
T
x
−
48
T
=
x
t
x
−
20
t
⇒
(
x
−
30
)
(
x
−
20
)
=
x
(
x
−
48
)
⇒
x
2
−
50
x
+
600
=
x
2
−
48
x
⇒
2
x
=
600
⇒
x
=
300
m
Thus, the length of the race is300 m
Ratio of speeds of A, B and
C
=
v
A
:
v
B
:
v
C
=
300
T
:
300
−
30
T
:
300
−
48
T
=
300
:
270
:
252
=
50
:
45
:
42
© examsnet.com
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