Advertisements
Advertisements
प्रश्न
An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.
Advertisements
उत्तर
Let the usual speed of aero plane be x km/hr. Then,
Increased speed of the aero plane = (x + 100)km/hr
Time taken by the aero plane under usual speed to cover 1200 km = `1200/x`hr
Time taken by the aero plane under increased speed to cover 1200 km = `1200/(x+100)hr`
Therefore,
`1200/x-1200/(x+100)=1`
`(1200(x+100)-1200x)/(x(x+100x))=1`
`(1200x+120000-1200x)/(x^2+100x)=1`
`12000/(x^2+100x)=1`
120000 = x2 + 100x
x2 + 100x - 120000 = 0
x2 - 300x + 400x - 120000 = 0
x(x - 300) + 400(x - 300) = 0
(x - 300)(x + 400) = 0
So, either
x - 300 = 0
x = 300
Or
x + 400 = 0
x = -400
But, the speed of the aero plane can never be negative.
Hence, the usual speed of train is x = 300 km/hr
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
(a + b)2x2 - 4abx - (a - b)2 = 0
The sum of the squares of the two consecutive odd positive integers as 394. Find them.
A girls is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.
If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:
x2 – (m + 2)x + (m + 5) = 0
One of the roots of equation 5m2 + 2m + k = 0 is `(-7)/5` Complete the following activity to find the value of 'k'.
Solve the following quadratic equation by factorisation.
2m (m − 24) = 50
If 2 is a root of the quadratic equation \[3 x^2 + px - 8 = 0\] and the quadratic equation \[4 x^2 - 2px + k = 0\] has equal roots, find the value of k.
If the equation x2 − ax + 1 = 0 has two distinct roots, then
If p and q are the roots of the equation x2 – px + q = 0, then ______.
Solve the following quadratic equation using formula method only
x2 - 6x + 4 = 0
Solve equation using factorisation method:
`6/x = 1 + x`
By increasing the speed of a car by 10 km/hr, the time of journey for a distance of 72 km. is reduced by 36 minutes. Find the original speed of the car.
Solve the following quadratic equation by factorisation method:
`x/(x + 1) + (x + 1)/x = (34)/(15') x ≠ 0, x ≠ -1`
In each of the following, determine whether the given values are solution of the given equation or not:
`x = 1/x = (13)/(6), x = (5)/(6), x = (4)/(3)`
The sum of two numbers is 9 and the sum of their squares is 41. Taking one number as x, form ail equation in x and solve it to find the numbers.
The hypotenuse of grassy land in the shape of a right triangle is 1 metre more than twice the shortest side. If the third side is 7 metres more than the shortest side, find the sides of the grassy land.
Two squares have sides A cm and (x + 4) cm. The sum of their areas is 656 sq. cm.Express this as an algebraic equation and solve it to find the sides of the squares.
Forty years hence, Mr. Pratap’s age will be the square of what it was 32 years ago. Find his present age.
