Question

Question 90

Ravi starts for his school at 8:20 am on his bicycle. If he travels at a speed of 10 km/h then he reaches his school late by 8 minutes but on travelling at 16 km/h, he reaches the school 10 minutes early. At what time does the school start?

Answer 1

Let the total distance = x km
Let the time taken by Ravi to reach the school at sharp time = l min.

If the speed of the bicycle is 10 km/ h then he reaches his school late by 8 min.
$\therefore \frac{x}{10}=l+\frac{8}{60}$
$\Rightarrow \frac{x}{10}=l+\frac{2}{15}...\left(i\right)$

If the speed of the bicycle is 16 km/ h then he reeach his school 10 min early.
$\therefore \frac{x}{16}=l-\frac{10}{60}\Rightarrow \frac{x}{16}=l-\frac{1}{6}...\left(ii\right)$

On solving Eqs. (i) and (ii), we get,
$\frac{x}{10}-\frac{x}{16}=\frac{2}{15}+\frac{1}{6}\Rightarrow \frac{8x-5x}{80}=\frac{4+5}{30}\Rightarrow \frac{3x}{80}=\frac{9}{30}\Rightarrow x=\frac{9\times 80}{30\times 3}=8$ km
Now, put $x=8inEq.\left(i\right),weget\frac{8}{10}=t+\frac{2}{15}\Rightarrow t=\frac{8}{10}-\frac{2}{15}=\frac{24-4}{30}\Rightarrow t=\frac{20}{30}=\frac{2}{3}h=\frac{2}{3}\times 60=40min$

So the time of school is 9:00 am.