CBSE Class 10 Maths Question Paper 2018 | Q16

Question 16: A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 km/h from the usual speed. Find its usual speed.

Video Explanation

Explanatory Answer | CBSE 2018 Math Paper Q16

Distance covered by the plane = 1500 km
Let the usual speed be s km/hr
Let the usual time taken be t hr

The plane left 30 minutes late and reached on time.
∴ Time taken in this instance = (t - 0.5) hr
Speed increased by 100 km/hr.
∴ Speed in this instance = (s + 100) km/hr

s × t = 1500 --------(1)
(s + 100) (t - 0.5) = 1500 ---------(2)
From (1) t = \\frac{1500}{s})

Substitute t = \\frac{1500}{s}) in (2)
(s + 100) (\\frac{1500}{s}) - 0.5) = 1500
(s + 100) (\\frac{1500 - 0.5s}{s})) = 1500
(s + 100) (1500 - 0.5s) = 1500s
1500s – 0.5s² + (1500 × 100) – 50s = 1500s
0.5s² + 50s - 150000 = 0
Or s² + 100s - 300000 = 0
s² + 600s – 500s - 300000 = 0
s(s + 600) - 500(s + 600) = 0
(s + 600) (s - 500) = 0
s = -600 or s = 500

Speed cannot be negative.
Hence, speed of the plane = 500 km/hr