Management Aptitude Test Dec 2013 Paper

(b) Let the distance covered be D km

and speed of train be x km/h.
∴ According to the question,

D

x

−

D

x+4

=

30

60

⇒

D(x+4−x)

x(x+4)

=

1

2

⇒ 8D = x2 + 4x    .....(i)
and

D

x−4

−

D

x

=

20

60

⇒ D[

(x+2−x)

x(x−2)

]=

1

3

⇒6D = x2 - 2x    .....(ii)
From Eqs. (i) and (ii), we get

x2+4x

8

=

x2−2x

6

⇒ 6x2 + 24x = 8x2 - 16x
⇒ 2x2 - 40x = 0
∴ 2x(x - 20) = 0
∴ x = 20 km/h
Hence, distance covered =

(20)2−2×20

6

= 60 km