Question : Ram walks at the speed of 12 km/hr and reaches his school 12 minutes late. If he walks at 16 km/hr, then he reaches 8 minutes before the scheduled time. What is the distance of his school from his house?
Option 1: 16 km
Option 2: 30 km
Option 3: 20 km
Option 4: 24 km
Correct Answer: 16 km
Solution :
Let distance between Ram's school and his house is D km and the actual time taken by Ram to reach his school from his home is $t$ minutes.
Distance = 12 × $\frac{t+12}{60}$ -----------(i)
Distance = 16 × $\frac{t-8}{60}$ -----------(ii)
From (i) and (ii),
12 × $\frac{t+12}{60}$ = 16 × $\frac{t-8}{60}$
⇒ $12t + 144 = 16t - 128$
⇒ $4t = 144+ 128$
⇒ $t = \frac{272}{4} = 68$ minutes
Distance = 12 × $\frac{t+12}{60}$
= 12 × $\frac{68+12}{60}$
= $\frac{80}{5}$
= 16 km
Hence, the correct answer is 16 km.
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