Advertisements
Advertisements
प्रश्न
Mukund has ₹ 50 more than Sagar. If the product of the amount they have is 15,000, then find the amount each has
उत्तर
Let Sagar possesses ₹ x.
∴ The amount Mukund possesses = ₹ (x + 50)
According to the given condition, the product of the amount they have is ₹ 15,000.
∴ x(x + 50) = 15000
∴ x2 + 50x – 15000 = 0
| -15000 |
| 150 -100 |
| 150 × (-100) = -15000 |
| 150 - 100 = 50 |
∴ x2 + 150x – 100x – 15000 = 0
∴ x(x + 150) – 100(x + 150) = 0
∴ (x + 150)(x – 100) = 0
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
x + 150 = 0 or x – 100 = 0
∴ x = –150 or x = 100
But, amount cannot be negative.
∴ x = 100 and x + 50 = 100 + 50 = 150
∴ The amount possessed by Sagar and Mukund are `100 and `150 respectively.
APPEARS IN
संबंधित प्रश्न
A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hour, it takes 2 hours less in the journey. Find the original speed of the train
Which of the following is a quadratic equation?
(a)` (x^2+1)=(2-x)^2+3` (b)` x^3-x^2=(x-1)^3`
(c) `2x^+3=(5+x)(2x-3)` (d) None of these
If the equation `9x^26kx+4=0` has equal roots then k =?
(a)1 or (b)-1 or 4 (c)1 or -4 (d)-1 or -4
The roots of the equation `2x^2-6x+3=0` are
(a) real, unequal and rational (b) real, unequal and irrational (c) real and equal (d) imaginary
The length of a rectangular field exceeds its breadth by 8 m and the area of the field is `240 m^2` . The breadth of the field is
(a) 20 m (b) 30 m (c) 12 m (d) 16 m
Find the value of k so that the quadratic equation` x^2-4kx+k=0`
has equal roots.
Find the value of k for which the quadratic equation `9x^2-3kx+k=0` has equal roots.
Decide whether the following equation is quadratic equation or not.
\[x + \frac{1}{x} = - 2\]
Decide whether the following equation is quadratic equation or not.
(m + 2) (m – 5) = 0
Vivek is older than Kishor by 5 years. The sum of the reciprocals of their ages is \[\frac{1}{6}\] Find their present ages.
Solve the following quadratic equation.
`1/(x + 5) = 1/x^2`
Solve the following quadratic equation.
x2 - 4x - 3 = 0
Solve any two of the following.
Solve : `3x+y=14 ; x-y=2`
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.
Write the quadratic equation 7 = 4x - x2 in the form of ax2+bx + c = 0.
Construct a word problem on quadratic equation, such that one of its answers is 20 (years, rupees, centimeter, etc.). Also, solve it.
Two water taps together can fill a tank in `1(7)/(8)` hours. The tap with longer diameter takes 2 hours less than the tap with a smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.
Solve for x : `1/(2a + b + 2x) =1/(2a) + 1/b + 1/(2x); x ≠ 0, x ≠ (−2a −b)/2`, a, b ≠ 0
In an orchard there are total 200 trees. If the number of trees in each column is more by 10 than the number of trees in each row, then find the number of trees in each row
If both the roots of the quadratic equation x2 – 2kx + k2 + k – 5 = 0 are less than 5, then k lies in the interval is ______.
