Q) In a flight of 600 km, an aircraft slowed down its speed due to bad weather. Its average speed for the trip reduced by 200 km/h from its usual speed and time of flight increased by 30 minutes. Find the scheduled duration of the flight.

(Q 34 A – 30/2/2 – CBSE 2026 Question Paper)

Ans: 

Step 1: Let’s consider the scheduled duration of flight is T hrs

∵ Flight distance, D = 600 km (given)

and we know that Speed = distance / time

∴ usual speed of aircraft, S = km/h ………. (i)

Step 2: Gy given condition, if speed reduced by 200 km/h, time of flight increases by 30 minutes or hrs

∴ S – 200 =

∴ S – 200 =

∴ S – 200 =

Step 3: By substituting values of S from equation (i), we get:

∴ 

∴ 

∴ (600 – 200 T) (2T + 1) = 1200 T

∴ 200 (3 –  T) (2T + 1) = 1200 T

∴ (3 –  T) (2T + 1) = 6 T

∴ 6 T + 3 –  2 T ² – T = 6 T

∴ 3 – 2 T ² – T = 0

∴ 2 T ² + T – 3 = 0

∴ 2 T ² + 3 T – 2T – 3 = 0

∴ T (2 T + 3) – (2T + 3) = 0

∴ (2 T + 3) (T – 1) = 0

∴ T = and T = 1

Step 4: Here, we reject T = because value of time taken can not be negative.

∴ T = 1 hr

Therefore, scheduled duration of the flight is 1 hr.

Check:
∵ Distance is 600 km and scheduled time is 1 hr
∴ Speed of aircraft is = 600 km/h
Now speed reduced by 200 km/h i.e. it becomes 600-200 = 400 km/h
∴ Now, the time taken to cover 600 km = = 1.5 hrs
∴ time increases by 1.5 – 1 = 0.5 hrs or 30 mins
∵ it meets the given condition, ∴ our answer is correct.

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