Question : If Abhi travels a certain distance at 6 km/hr, he reaches his destination 12 minutes early, but if he travels at 4 km/hr, he reaches his destination 10 minutes late. The speed (in km/hr) at which he should travel to reach his destination on time is _____.
Option 1: $5 \frac{1}{4}$
Option 2: $5 \frac{1}{8}$
Option 3: $4 \frac{3}{7}$
Option 4: $4 \frac{5}{7}$
Correct Answer: $4 \frac{5}{7}$
Solution :
Given :
Abhi's original speed = 6 km/hr
Abhi's new speed = 4 km/hr
Let the right time for the man to cover his journey be $x$ min.
According to the question,
$ 6\ \times \frac{x\ -\ 12}{60}\ =\ 4\ \times\ \frac{x\ -\ 12}{60}$
$\Rightarrow 3(x\ -\ 12)\ =\ 2(x\ +\ 10)$
$\Rightarrow 3x\ -\ 36\ =\ 2x\ +\ 20$
$\Rightarrow x\ =\ 56$
So, Speed of the man = $\frac{6(56- 12)}{60\ \times \frac{56}{60}} = \frac{6\times 44}{56} = \frac{33}{7} = 4\tfrac{5}{7}$ km/hr
Hence, the correct answer is $4\tfrac{5}{7}$.
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