A person from the top of a hill observes a vehicle moving towards him at a uniform speed. It takes 10 minutes for the angle of depression to change from 45° to 60°. After this the time required by the vehicle to reach the bottom of the hill is

Question

Question

This question was previously asked in

SSC CGL Tier-II Quant Previous Paper 17 (Held On: 1 December 2016)

Attempt in App

Answer 1

Calculation:

CD = 10 unit

In Δ ABC

tan 45 = AB/BC

BC = AB --- (1)

In ΔABD

tan 60 = AB/BD

⇒ √3 = AB/BD

⇒ AB = √3 BD

BC = √3 BD [From equation (1)]

BC = BD + CD

⇒ √3 BD – BD = CD

⇒ BD (√3 – 1) = 10

⇒ BD = 10/(√3 – 1) × [(√3 + 1)/(√3 + 1)]

⇒ BD = 10 (√3 + 1)/2

⇒ BD = 5 (1.732 + 1)

⇒ BD = 5 × 2.732

⇒ BD = 13.66 unit

⇒ 10 unit = 10 min

⇒ 13.66 unit = 13 min 40 sec

Short Trick:

(√3 – 1) unit = 10 min

1 unit = 10/(√3 - 1) × [(√3 + 1)/(√3 + 1)]

⇒ 1 unit = 10 (√3 + 1)/2 = 5 (1.732 + 1) = 5 × 2.732 = 13.66

⇒ 13.66 = 13 min 40 sec