Management Aptitude Test 2014 Paper

(b) Let the time taken by Ram to finish the race = t min
Case I
Ram gives Shyam a start of 200 m and beats him by 30 s, i.e.,

1

2

min.
∴ Speed of Ram =

2000

t

and, speed of Shyam =

1800

t+ 1 2

Case II
Here, Ram gives Shyam a start of 3 min and losses to Shyam by 1000 m.
∴ Time taken by Shyam - Time taken by Ram = 3 m

2000

1800 t+ 1 2

−

1000

2000 t

= 3
⇒

2000

1800×2 2t+1

−

t

2

= 3
⇒

2000×(2t+1)

1800×2

−

t

2

= 3
⇒

5

9

(2t+1)−

t

2

= 3
⇒

10(2t+1)−9t

18

= 3
⇒ 20t + 10 - 9t = 18 x 3
⇒ 11t = 54 - 10
∴ t =

44

10

= 4min
So, time taken by Ram to finish the race is 4 min.
Again, speed of Shyam
=

1800

t+ 1 2

⇒

1800

4+ 1 2

=

1800

8+1

×2
= 400 m/min
So, to cover 2000 m Shyam will take 5 min.