Question

A person covers a distance from point A to B by his car with the speed of x km/hr. If he drives at the speed of (x + 8) km/hr, then he takes 2 hours less. But if he drives (x – 12) km/hr, then he takes 4 hours more. Find the time to travel from point A to B at speed of (x + 3) km/hr?
1. 15.5 hrs
2. 24.4 hrs
3. 19.2 hrs
4. 21.4 hrs
5. None of these

Answer 1

Correct Answer - Option 3 : 19.2 hrs

Given:

If speed of car = x km/hr, time = T hrs

If speed of car = (x + 8) km/hr, time = (T -2) hrs

If speed of car = (x – 12) km/hr, time = (T + 4) hrs

Formula used:

Distance = Time × Speed

Calculation:

Distance = xT     ----- (1)

Distance = (x + 8)(T – 2)       ----- (2)

Distance = (x – 12)(T + 4)        ------- (3)

According to question –

From (1) & (2):

⇒ xT = (x + 8)(T – 2)

⇒ xT = xT + 8T – 2x – 16

⇒ 8T – 2x = 16       ----- (4)

From (1) & (3):

⇒ xT = (x – 12)(T + 4)

⇒ xT = xT – 12T + 4x – 48

⇒ -12T + 4x = 48      ---- (5)

Multiplying equation (4) by 2 and adding to equation (5) –

⇒ (16T – 12T) = (32 + 48)

⇒ 4T = 80

⇒ T = 20 hours

Put this value in equation (4) we get,

⇒ 8(20) – 2x = 16

⇒ 160 – 2x = 16

⇒ 2x = 144

⇒ x = 72

∴ Distance = xT = 72 × 20 = 1440 km

⇒ Distance between A and B = 1440 km

And (x + 3) = 75 km/hr

∴ Time taken to travel from A to B with speed of 75 km/hr = 1440/75 = 19.2 hrs