Advertisements
Advertisements
प्रश्न
Ranjana wants to distribute 540 oranges among some students. If 30 students were more each would get 3 oranges less. Find the number of students.
उत्तर
Let the total number of students be x.
Total oranges = 540
Orange each student gets will be `540/x`.
If 30 more students are there so, the total number of students will be x + 30.
Number of oranges per person will be `540/(x + 30)`.
If 30 students were more each would get 3 oranges less = `540/x - 3`
`540/(x + 30) = 540/x - 3`
⇒ `3 = 540(1/x - 1/(x + 30))`
⇒ `1 = 540/3 ((x + 30 - x)/(x(x + 30)))`
⇒ `1 = 180 ((30)/(x^2 + 30x))`
⇒ x2 + 30x = 5400
⇒ x2 + 30x − 5400 = 0
⇒ x2 + 90x − 60x − 5400 = 0
⇒ x(x + 90) − 60(x + 90) = 0
⇒ (x + 90)(x − 60) = 0
⇒ x + 90 = 0 or x – 60 = 0
⇒ x = – 90 or x = 60
But number of students cannot be negative so, the number of students is 60.
संबंधित प्रश्न
If one of the roots of the quadratic equation x2 - 11x + k = 0 is 9, then find the value of k
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 product of the roots of the equation `x^2-3x+k=10` is-2 then the value of k is
(a) -2 (b) -8 (c) 8 (d) 12
If the roots of the equation` ax^2+bx+c=0` are equal then c=?
(a)`b/(2a)` (b) `b/(2a)` (c) `-b^2/(4a)` (d) `B^2/(4a)`
The roots of `ax^2+bx+c=0`,a≠0 are real and unequal, if `(b^2-4ac)` is
(a)>0 (b)=0 (c)<0 (d)none of these
The roots of the quadratic equation `2x^2-x-6=0`
(a)`-2, 3/2` (b) `2, -3/2`
(c)` -2, 3/2` (d) `2, 3/2`
Show the x= -3 is a solution of `x^2+6x+9=0`
If the quadratic equation `px^2-2sqrt5px+15=0` has two equal roots then find the value of p.
If one zero of the polynomial `x^2-4x+1 is (2+sqrt3)` write the other zero.
Solve `3x^2+5sqrt5x-10=0`
Decide whether the following equation is quadratic equation or not.
`"y"^2 + 1/"y" = 2`
The Sum of squares of 2 consecutive natural even numbers is 244; find the numbers.
Suyash scored 10 marks more in second test than that in the first. 5 times the score of the second test is the same as square of the score in the first test. Find his score in the first test.
Pratik takes 8 hours to travel 36 km downstream and return to the same spot. The speed of boat in still water is 12 km. per hour. Find the speed of water current.
Which of the following is a quadratic equation ?
If P(y) = y² - 2y + 5, find P(2) .
For the quadratic equation 3x2 + 2x - 1 = 0 , find the value of the discriminant.
Mukund has ₹ 50 more than Sagar. If the product of the amount they have is 15,000, then find the amount each has
In a right-angled triangle, altitude is 2 cm longer than its base. Find the dimensions of the right-angled triangle given that the length of its hypotenuse is 10 cm.
