Advertisements
Advertisements
प्रश्न
A teacher on attempting to arrange the students for mass drill in the form of solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.
Advertisements
उत्तर
Let there be x rows.
Then, the number of students in each row will also be x.
∴ Total number of students =(x^2+24)
According to the question:
`(x+1)^2-25=x^2+24`
⇒`x^2+2x+1-25-x^2-24=0`
⇒`2x-48=0`
⇒`2x=48`
⇒`x=24`
∴ Total number of students `=24^2+24=576+24=600`
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`a/(x-a)+b/(x-b)=(2c)/(x-c)`
A two digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.
A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.
Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0.
Find the values of k for which the roots are real and equal in each of the following equation:
\[kx\left( x - 2\sqrt{5} \right) + 10 = 0\]
If the equation x2 − ax + 1 = 0 has two distinct roots, then
Solve the following equation: 4x2 - 13x - 12 = 0
Solve the following quadratic equation using formula method only
6x2 + 7x - 10 = 0
Find two consecutive natural numbers whose squares have the sum 221.
In each of the following, determine whether the given values are solution of the given equation or not:
x2 + x + 1 = 0; x = 0; x = 1
Solve the following equation by factorization
x(6x – 1) = 35
Solve the following equation by factorization
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2(1)/(2)`
Find two consecutive odd integers such that the sum of their squares is 394.
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
Solve the following equation by factorisation :
3x2 + 11x + 10 = 0
Solve the following equation by factorisation :
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
Divide 16 into two parts such that the twice the square of the larger part exceeds the square of the smaller part by 164.
If the sum of the roots of the quadratic equation ky2 – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.
If the discriminant of the quadratic equation 3x2 - 2x + c = 0 is 16, then the value of c is ______.
The product of two integers is –18; the integers are ______.
