Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let the original speed of train be x km/hr. Then,
Increased speed of the train = (x + 15)km/hr
Time taken by the train under usual speed to cover 90 km = `90/x`hr
Time taken by the train under increased speed to cover 90 km = `90/(x+15)`hr
Therefore,
`90/x-90/(x+15)=30/60`
`(90(x+15)-90x)/(x(x+15))=1/2`
`(90x+1350-90x)/(x^2+15x)=1/2`
`1350/(x^2+15x)=1/2`
1350(2) = x2 + 15x
2700 = x2 + 15x
x2 + 15x - 2700 = 0
x2 - 45x + 60x - 2700 = 0
x(x - 45) + 60(x - 45) = 0
(x - 45)(x + 60) = 0
So, either
x - 45 = 0
x = 45
Or
x + 60 = 0
x = -60
But, the speed of the train can never be negative.
Hence, the original speed of train is x = 45 km/hr
APPEARS IN
संबंधित प्रश्न
Solve for x : `(x+1)/(x-1)+(x-1)/(x+2)=4-(2x+3)/(x-2);x!=1,-2,2`
Solve the following quadratic equations by factorization:
(2x + 3)(3x − 7) = 0
Solve the following quadratic equations by factorization:
`1/(x-2)+2/(x-1)=6/x` , x ≠ 0
A two digit number is such that the product of the digits is 16. When 54 is subtracted from the number the digits are interchanged. Find the number
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.
Solve each of the following equations by factorization:
x(x – 5) = 24
Solve the following quadratic equations by factorization:
`(2x – 3)^2 = 49`
The sum of the squares to two consecutive positive odd numbers is 514. Find the numbers.
The sum of two natural numbers is 9 and the sum of their reciprocals is `1/2`. Find the numbers .
Solve the following quadratic equation by factorisation.
\[6x - \frac{2}{x} = 1\]
Solve the following quadratic equation by factorisation.
2m (m − 24) = 50
If p and q are the roots of the equation x2 – px + q = 0, then ______.
If \[\left( a^2 + b^2 \right) x^2 + 2\left( ab + bd \right)x + c^2 + d^2 = 0\] has no real roots, then
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.
Solve the following equation:
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 5/2 , x ≠-1/2`
A farmer wishes to grow a 100m2 rectangular vegetable garden. Since he was with him only 30m barbed wire, he fences 3 sides of the rectangular garden letting the compound of his house to act as the 4th side. Find the dimensions of his garden .
Solve the following by reducing them to quadratic equations:
`sqrt(x/(1 -x)) + sqrt((1 - x)/x) = (13)/(6)`.
Solve the following equation by factorization
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
A school bus transported an excursion party to a picnic spot 150 km away. While returning, it was raining and the bus had to reduce its speed by 5 km/hr, and it took one hour longer to make the return trip. Find the time taken to return.
Find the roots of the following quadratic equation by the factorisation method:
`2/5x^2 - x - 3/5 = 0`
