Advertisements
Advertisements
प्रश्न
A passenger train takes one hour less for a journey of 150 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 train be x km/hr then
Increased speed of the train = (x + 5)km/hr
Time taken by the train under usual speed to cover 150km = `150/x`hr
Time taken by the train under increased speed to cover 150km = `150/(x + 5)`hr
Therefore,
`150/x-150/(x+5)=1`
`(150(x+5)-150x)/(x(x+5))=1`
`(150x+750-150)/(x^2+5x)=1`
`750/(x^2+5x)=1`
750 = x2 + 5x
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 train can never be negative.
Hence, the usual speed of train is x = 25km/hr
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a`
The sum of two numbers is 48 and their product is 432. Find the numbers?
Solve:
`1/(x + 1) - 2/(x + 2) = 3/(x + 3) - 4/(x + 4)`
Solve each of the following equations by factorization:
`x=(3x+1)/(4x)`
`2x^2+5x-3=0`
The sum of a natural number and its square is 156. Find the number.
The sum of the squares two consecutive multiples of 7 is 1225. Find the multiples.
The sum of two natural numbers is 20 while their difference is 4. Find the numbers.
Solve the following quadratic equations by factorization:\[\frac{1}{x - 3} + \frac{2}{x - 2} = \frac{8}{x}; x \neq 0, 2, 3\]
The value of c for which the equation ax2 + 2bx + c = 0 has equal roots is
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.
The values of k for which the quadratic equation \[16 x^2 + 4kx + 9 = 0\] has real and equal roots are
Solve the following equation : `"x"^2 - 4 sqrt 2 "x" + 6 = 0 `
A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.
Solve the following quadratic equation by factorisation:
(2x + 3) (3x - 7) = 0
Solve the following quadratic equation by factorisation:
9x2 - 3x - 2 = 0
If the product of two consecutive even integers is 224, find the integers.
At an annual function of a school, each student gives the gift to every other student. If the number of gifts is 1980, find the number of students.
Complete the following activity to solve the given quadratic equation by factorization method.
Activity: x2 + 8x – 20 = 0
x2 + ( __ ) – 2x – 20 = 0
x (x + 10) – ( __ ) (x + 10) = 0
(x + 10) ( ____ ) = 0
x = ___ or x = 2
Find the roots of the following quadratic equation by the factorisation method:
`2x^2 + 5/3x - 2 = 0`
