Advertisements
Advertisements
प्रश्न
A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.
Advertisements
उत्तर
Let the usual speed of the passenger train be x km/hr. Then,
Increased speed of the passenger train = (x + 5) km/hr
Time taken by the train under usual speed to cover 300 km = `300/x`hr
Time taken by the train under increased speed to cover 300 k m = `300/(x + 5)`hr
Therefore,
`300/x-300/(x+5)=2`
`(300(x+5)-300x)/(x(x+5))=2`
`(300x+1500-300x)/(x^2+5x)=2`
`1500/(x^2+5x)=2`
1500 = 2(x2 + 5x)
1500 = 2x2 + 10x
2x2 + 10 - 1500 = 0
2(x2 + 5x - 750) = 0
x2 + 5x - 750 = 0
x2 - 25x + 30x - 750 = 0
x(x - 25) + 30(x - 25) = 0
(x - 25)(x + 30) = 0
So, either
x - 25 = 0
x = 25
Or
x + 30 = 0
x -30
But, the speed of the passenger train can never be negative.
Hence, the usual speed of passenger train is x = 25 km/hr
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`x^2-4sqrt2x+6=0`
A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for a journey. Find the original speed of the train.
An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?
Solve the following quadratic equations by factorization:
`4(2x – 3)^2 – (2x – 3) – 14 = 0`
Solve the following quadratic equations by factorization:
`100/x-100/(x+5)=1`
Find two consecutive multiples of 3 whose product is 648.
Solve the following quadratic equation by factorisation.
x2 – 15x + 54 = 0
Solve the following quadratic equation by factorisation.
\[6x - \frac{2}{x} = 1\]
The distance between Akola and Bhusawal is 168 km. An express train takes 1 hour less than a passenger train to cover the distance. Find the average speed of each train if the average speed of the express train is more by 14 km/hr than the speed of the passenger train.
Solve the following quadratic equations by factorization: \[\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 4 - \frac{2x + 3}{x - 2}; x \neq 1, - 2, 2\]
Write the sum of real roots of the equation x2 + |x| − 6 = 0.
If the equation x2 − bx + 1 = 0 does not possess real roots, then
The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.
The area of the isosceles triangle is 60 cm2, and the length of each one of its equal side is 13cm. Find its base.
Solve the following by reducing them to quadratic equations:
`((7y - 1)/y)^2 - 3 ((7y - 1)/y) - 18 = 0, y ≠ 0`
A man spent Rs. 2800 on buying a number of plants priced at Rs x each. Because of the number involved, the supplier reduced the price of each plant by Rupee 1.The man finally paid Rs. 2730 and received 10 more plants. Find x.
Which of the following are the roots of the quadratic equation, x2 – 9x + 20 = 0 by factorisation?
Solve the following quadratic equation by factorisation method:
x2 + x – 20 = 0
4x2 – 9 = 0 implies x is equal to ______.
