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A man walks from his house to the Railway station to catch a train, which is running as per schedule. If he walks at $6 \frac{km}{h}$ , $6 \frac{km}{h}$ he misses the train by 99 minutes. However, if he walks at $7 \frac{km}{h}$ , $7 \frac{km}{h}$ He reaches the station 6 minutes before the departure of the train. The distance of his home to the Railway Station is:

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2 km

10.5 km

1.05 km

1.25 km

answer is B.

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Detailed Solution

Concept- Calculating the distance by using the time distance and speed

D = V \times T

,
D = distance
V = speed
T = time
Suppose, the distance between the railway and home is d,
First case,

V = 6 \frac{km}{h},

T + \frac{9}{60}, time conversion that' s why we divided by 60

D = 6 \times (t + \frac{9}{60})

Now, second case,

V = 7 \frac{km}{h}

Time is T - \frac{6}{60}

So,

D = 7 \times (T - \frac{6}{60})

Equating both the equations,

6 \times (T + \frac{9}{60}) = 7 \times (T - \frac{6}{60})

6 (T + 0.15) = 7 (T - 0.1)

6 T + 0.9 = 7 T - 0.7

6 T - 7 T = - 0.7 - 0.9

- T = - 1.6

T = 1.6

Now, put the value of T in equation

D = 7 \times (T - \frac{6}{60})

D = 7 \times (1.6 + 0.1)

D = 7 \times 1.5 = 10.5 km

Hence, the correct option is 2.

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