Question 32 (Choice 2) - CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at May 29, 2023 by Teachoo

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

Question 32 (Choice 2) In a flight of 600km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr from its usual speed and the time of the flight increased by 30 min. Find the scheduled duration of the flight.Let the speed of aircarft be x km/hr
Normal speed
Distance = 600 km
Speed = x km/hr
Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑇𝑖𝑚𝑒
x = 600/𝑇𝑖𝑚𝑒
Time = 𝟔𝟎𝟎/𝒙
Speed reduced by 200 km/h
Distance = 600 km
Speed = (x − 200) km/hr
Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑇𝑖𝑚𝑒
x − 200 = 𝟔𝟎𝟎/𝑻𝒊𝒎𝒆
Time = 𝟔𝟎𝟎/(𝒙 − 𝟐𝟎𝟎)
Given that
Its average speed for the trip was reduced by 200 km/hr from its usual speed and the time of the flight increased by 30 min
Time when speed reduced − Time normal = 30 minutes
Time when speed reduced − Time normal = 𝟏/𝟐 hour
𝟔𝟎𝟎/(𝒙 − 𝟐𝟎𝟎)−𝟔𝟎𝟎/𝒙=𝟏/𝟐
(600𝑥 − 600(𝑥 − 200))/(𝑥(𝑥 − 200))=1/2
(600𝑥 − 600𝑥 + 120000)/(𝑥^2 − 200𝑥)=1/2
120000/(𝑥^2 − 200𝑥)=1/2
2 × 120000 = x2 − 200x
240000 = x2 − 200x
x2 – 200x − 240000 = 0
x2 − 200x – 240000 = 0
Comparing with ax2 + bx + c = 0
a = 1, b = −200, c = −240000
Roots of the equation are given by
x = (− 𝑏 ± √(𝑏^2 − 4𝑎𝑐))/2𝑎
Putting values
x = (−(−200) ± √(〖(−200)〗^2 − 4 × 1 × (−240000) ))/(2 × 1)
x = (200 ± √(40000 + 4 × 240000))/2
x = (200 ± √(40000 + 960000))/2
x = (200 ± √1000000)/2
x = (200 ± √(〖10〗^6 ))/2
x = (𝟐𝟎𝟎 ± 𝟏𝟎𝟎𝟎)/𝟐
Hence x = 600, x = –400 are the roots of the equation
x = (200 + 1000)/2
x = 1200/2
x = 600
x = (200 − 1000)/2
x = (−800)/2
x = –400We know that Speed of flight = x
So, x cannot be negative
∴ x = 600 is the solution
So, Speed of flight = x = 600 km/hr
But, we need to find the scheduled duration of the flight.
Scheduled Duration = Time = 𝟔𝟎𝟎/𝒙
= 600/600
= 1 hour

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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