2019 Class 10 Math Sample Paper | Q23A

This 2019 CBSE class 10 Maths 4 mark question is from Quadratic Equations. An easy 4 mark question in CBSE class 10 sample question paper. Concept: Speed Distance Time - speed of train. A standard NCERT text book question.

Question 23A: A train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/h from its usual speed. Find the usual speed of the train.

Video Explanation

Explanatory Answer

Let 's' be the usual speed of the train.
Time = \\frac{\text{Distance}}{\text{Speed}})
Time taken to cover 300 km at s km/h = \\frac{300}{s}) hours ------ (1)
Time taken to cover 300 km at (s + 5) km/h = \\frac{300}{s + 5}) hours ------ (2)

The train takes 2 hours lesser to cover the same distance after its speed is increased by 5 kmph:
(1) - (2) = 2
\\frac{300}{s}) - \\frac{300}{s + 5}) = 2
\\frac{300(s + 5) − 300s}{s(s + 5)}) = 2
1500 = 2s² + 10s
s² + 5s - 750 = 0

Factorize the Quadratic Equation to find the value of s
s² + 30s – 25s - 750 = 0
(s – 25)(s + 30) = 0
s = 25 or -30

Speed cannot be negative.
∴The usual speed of the train, s = 25 km/h