CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard

Question 37 (OR 1st question) - CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard

Last updated at Oct. 9, 2019 by Teachoo

A train covers a distance of 360 km at a uniform speed. Had the speed been 5 km/hour more, it would have taken 48 minutes less for the journey. Find the original speed of the train.

Note
: This
is similar
to Ex 4.3, 8 of NCERT – Chapter 4 Class 10

Question 37 (OR 1st question) A train covers a distance of 360 km at a uniform speed. Had the speed been 5 km/hour more, it would have taken 48 minutes less for the journey. Find the original speed of the train.
Let the speed of train be x km/hr
Normal speed
Distance = 360 km
Speed = x km/hr
Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑇𝑖𝑚𝑒
x = 360/𝑇𝑖𝑚𝑒
Time = 360/𝑥
Speed 5 km/h more
Distance = 360 km
Speed = (x + 5) km/hr
Time = (360/𝑥 " – " 48/60) hours
Speed = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑇𝑖𝑚𝑒
x + 5 = 360/((360/𝑥 " – " 48/60) )
(x + 5) (360/𝑥 " – " 48/60) = 360
From (1)
(x + 5) (360/𝑥 " – " 48/60) = 360
(x + 5) (360/𝑥 " – " 4/5) = 360
(x + 5) ((5 × 360 − 4𝑥)/5𝑥) = 360
(x + 5) ((1800 − 4𝑥)/5𝑥) = 360
(x + 5) (1800 – 4x) = 360 × 5x
x(1800 – 4x) + 5(1800 – 4x) = 1800x
1800x – 4x2 + 5(1800) – 20x = 1800x
1800x – 4x2 + 9000 – 20x = 1800x
1800x – 4x2 + 9000 – 20x – 1800x = 0
– 4x2 – 20x + 9000 = 0
4x2 + 20x – 9000 = 0
4(x2 + 5x – 2250) = 0
x2 + 5x – 2250 = 0
Comparing with ax2 + bx + c = 0
a = 1, b = 5, c = –2250
Roots of the equation are given by
x = (− 𝑏 ± √(𝑏^2 − 4𝑎𝑐))/2𝑎
Putting values
x = (−5 ± √(5^2 − 4 × 1 × (−2250) ))/(2 × 1)
x = (−5 ± √(25 + 4 × 2250 ))/2
x = (−5 ± √(25 + 9000))/2
x = (−5 ± √9025)/2
x = (−5 ± √(5^2×〖19〗^2 ))/2
x = (−5 ± 5×19)/2
x = (−5 ± 95)/2
x = (−5 + 95)/2
x = 90/2
x = 45
x = (−5 − 95)/2
x = (−100)/2
x = –50
Hence x = 45, x = –50 are the roots of the equation
We know that Speed of train = x
So, x cannot be negative
∴ x = 45 is the solution
So, Speed of train = x = 45 km/hr

CBSE Class 10 Sample Paper for 2020 Boards - Maths Standard

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.