Question

In the given diagram (not drawn to scale), railway stations A, B, C, P and Q are connected by straight tracks. Track PQ is parallel to BC. The time taken by a train travelling at 90km/hr to reach B from A by the shortest route is:

विकल्प

• 8 minutes

• 12 minutes

• 16.8 minutes

• 20 minutes

Answer 1

20 minutes

Explanation:

PQ || BC

So, ΔAPQ ∼ ΔABC and `(PQ)/(BC) = 20/50 = 2/5`. 

Hence, `(AP)/(AB) = 2/5`.

Let AP = x and PB = 18.

So, AB = x + 18 and `x/(x + 18) = 2/5` 

⇒ 5x = 2x + 36

⇒ x = 12 km

So, AB = 30 km. 

Time = `"Distance"/"Speed"`

= `(30  km)/(90  km) xx hr^-1` 

= `1/3 hr`

= 20 minutes