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Management Aptitude Test Dec 2013 Paper

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Question : 116 of 200

Marks: +1, -0

A man covers a certain distance

65 km
60 km
70 km
75 km

Solution:

(b) Let the distance covered be D km

and speed of train be x km/h.

∴ According to the question,

\frac{D}{x} - \frac{D}{x+4} = \frac{30}{60}

⇒

\frac{D(x+4-x)}{x(x+4)} = \frac{1}{2}

⇒ 8D =

x^2

+ 4x .....(i)

and

\frac{D}{x-4} - \frac{D}{x} = \frac{20}{60}

⇒

D\left[\frac{x+2-x}{x(x-2)}\right] = \frac{1}{3}

⇒6D =

x^2

- 2x .....(ii)

From Eqs. (i) and (ii), we get

\frac{x^2+4x}{8}

=

\frac{x^2-2x}{6}

⇒ 6

x^2

+ 24x = 8

x^2

- 16x

⇒ 2

x^2

- 40x = 0

∴ 2x(x - 20) = 0

∴ x = 20 km/h

Hence, distance covered =

\frac{(20)^2 - 2 \times 20}{6}

= 60 km

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