Aman walks at 5 km/hr and reaches his school 28 minutes late. If he walks at 8 km/hr, then he reaches 35 minutes before the scheduled time. What is the distance from his school to his house?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 14 km.
Let the distance be D kilometers and the time be T
Aman walks at 5 km/hr and reaches his school 28 minutes late
D/5 = T + 7/15
⇒ T = D/5 - 7/15
If he walks at 8 km/hr, then he reaches 35 minutes before the scheduled time
D/8 = T - 7/12
⇒ T = D/8 + 7/12
⇒ D/5 - 7/15 = D/8 + 7/12
⇒ D/5 - D/8 = 7/12 + 7/15
⇒ 3D/40 = 70/120 + 56/120
⇒ 3D/40 = 126/120
⇒ 3D = 42
⇒ D = 14
Thus, the distance is 14 km