Question : If I walk at $\frac{7}{6}$th of my usual speed, then I reach my office 15 minutes early. What is the usual time taken (in minutes) by me to reach the office?
Option 1: 60
Option 2: 75
Option 3: 90
Option 4: 105
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Correct Answer: 105
Solution :
Let the usual time, speed, and distance be $t$ hours, $u$ km/hr, and $d$ km, respectively.
$\frac{d}{u}=t$
Time taken by current speed – time taken by usual speed = $\frac{15}{60}$
$⇒\frac{d}{u}-\frac{d}{\frac{7u}{6}}=\frac{15}{60}$
$⇒t-\frac{6t}{7}=\frac{1}{4}$
$⇒\frac{t}{7} =\frac{1}{4}$
$⇒t=\frac{7}{4}$ hours
$\therefore t=\frac{7}{4}\times 60= 105$ minutes
Hence, the correct answer is 105.
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