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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Question : A journey takes 4 hours 30 minutes at a speed of 60 km/h. If the speed is 15 m/s, then the journey will take:
Option 1: 5 hours
Option 2: 5 hours 30 minutes
Option 3: 6 hours
Option 4: 6 hours 15 minutes
Question : The speed of a train including stoppages is 75 kmph and excluding stoppages, the speed of the train is 90 kmph. For how many minutes does the train stop per hour?
Option 1: 10 minutes
Option 2: 15 minutes
Option 3: 20 minutes
Option 4: 11 minutes
Question : Find the value of $\cos 0^{\circ}+\cos 30^{\circ}-\tan 45^{\circ}+\operatorname{cosec} 60^{\circ}+\cot 90^{\circ}$.
Option 1: $\frac{7}{6 \sqrt{3}}$
Option 2: $\frac{\sqrt{3}}{6}$
Option 3: $\frac{7}{6}$
Option 4: $\frac{7}{2 \sqrt{3}}$
Question : If $\sec A=\frac{17}{15}$, then what is the value of $\cot A$?
Option 1: $\frac{15}{21}$
Option 2: $\frac{15}{7}$
Option 3: $\frac{8}{15}$
Option 4: $\frac{15}{8}$
Question : Find the fourth proportion of the numbers $\frac{1}{3}{rd}$ of 15, $\frac{4}{5}{th}$ of 25, $\frac{3}{7}{th}$ of 35:
Option 1: 65
Option 2: 55
Option 3: 60
Option 4: 50
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