. If the speed of a train is increased by 5 km/h from its
normal speed it would have taken 2 h less to cover
300 km. What is its normal speed?
(1) 20 km/h
(2) 25 km/h
(3) 30 km/h
(4) 45 km/h
(5) None of these
Answers
Answer:
Answer is (2) 25 km/h
Step-by-step explanation:
Distance to be covered = 300 km,
Let normal speed of the train = n kmph. Normal duration of the journey, T = 300/n hours.
With increased speed of 5 kmhr journey time = 300/(n+5) = T-2.
T = 300/n …(1)
T-2 = 300/(n+5) …(2)
Subtract (2) from (1) to get
2 = 300/n -300/(n+5), or
2n(n+5) = 300(n+5) - 300n = 1500, or
n(n+5) = 750, or
n^2+5n-750 = 0
(n+30)(n-25) = 0
n = 25 kmph.
The normal speed of the train is 25 kmph.
Answer:
Normal speed = 25 km/hr
Step-by-step explanation:
Let the normal speed be x
then time = 300/x h
now, after increasing speed by 5km/h time = 300/x+5
here, 300/x +5 = 300/x - 2
= 300/x +5 = 300 - 2x/x
= 300x = (300 - 2x) (x + 5)
= 300x = 300x + 1500 - 2x² - 10x
= 300x = 290x + 1500 - 2x²
= 300x - 290x + 2x² = 1500
= 10x + 2x² = 1500
= 2x (5 + x) = 1500
= x² + 5x = 750
= x² + 2 × x × 5/2 + (5/2)² = 750 + 25/4 [adding both side by (5/2)²
= (x + 5/2)² = 3000 + 25/4
= x + 5/2 = √(3025/4)
= x + 5/2 = ± 55/2
here, Is two part 1st positive and 2nd negative
= x + 5/2 = 55/2 = x + 5/2 = -55/2
= x = 55/2 - 5/2 = x = -55/2 - 5/2
= x = 25 km/hr = x = -30 km/hr
But speed can't be in negative.
∴ Normal speed = 25 km/hr
hope it will help you.