CMAT 2015 Solved Question Paper

(a) Since, Arman beats Bhuvan by 100 m.
∴ Ratio of speeds of Arman and Bhuvan = 1000: 900 = 10:9
Let speed of Arman be 10x m/s and speed of Bhuvan be 9x m/s.
Distance covered = 1 km = 1000 m
Time taken by Arman =

1000

10x

s
Time taken by Bhuvan =

1000

9x

s
According to the question,
‌‌‌‌‌‌

1000

10x

+10=

1000

9x

⇒

1000

10x

−

1000

9x

=−10
⇒ 1000(

1

9x

−

1

10x

)=10
⇒ 1000(

10−9

90x

) = 10
⇒

1000

90x

= 10
⇒ 1000 = 10 × (90x)
∴ x =

1000

900

=

10

9

Required time =

1000

10

×

9

10

s =

9000

100

= 90 s = 1 min 30s