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:
(2x + 3)(3x − 7) = 0
Solve the following quadratic equations by factorization:
`x^2-4sqrt2x+6=0`
Let us find two natural numbers which differ by 3 and whose squares have the sum 117.
Solve the following quadratic equations by factorization:
`(2x – 3)^2 = 49`
`x^2+8x-2=0`
Find the value of k for which the following equations have real and equal roots:
\[x^2 - 2\left( k + 1 \right)x + k^2 = 0\]
The value of c for which the equation ax2 + 2bx + c = 0 has equal roots is
If \[x^2 + k\left( 4x + k - 1 \right) + 2 = 0\] has equal roots, then k =
Solve the following quadratic equation using formula method only
x2 - 6x + 4 = 0
A two digit number is such that its product of its digit is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.
A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.
The hypotenuse of a grassy land in the shape of a right triangle is 1 m more than twice the shortest side. If the third side is 7m more than the shortest side, find the sides of the grassy land.
A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and Solve it to find the original cost of the books.
Solve for x:
`(x + 1/x)^2 - (3)/(2)(x - 1/x)-4` = 0.
In each of the following, determine whether the given values are solution of the given equation or not:
x2 - 3`sqrt(3)` + 6 = 0; x = `sqrt(3)`, x = -2`sqrt(3)`
Solve the following equation by factorization
`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`
Harish made a rectangular garden, with its length 5 metres more than its width. The next year, he increased the length by 3 metres and decreased the width by 2 metres. If the area of the second garden was 119 sq m, was the second garden larger or smaller ?
Two natural numbers are in the ratio 3 : 4. Find the numbers if the difference between their squares is 175.
A farmer wishes to grow a 100 m2 rectangular vegetable garden. Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall of his house act as the fourth side fence. Find the dimensions of his garden.
Solve the following quadratic equation by factorisation method:
x2 + x – 20 = 0
