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
Find two consecutive positive integers, sum of whose squares is 365.
Solve for x
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 2, "where x" != -1/2, 1`
Solve the following quadratic equations by factorization:
`(x-1)/(2x+1)+(2x+1)/(x-1)=5/2` , x ≠ -1/2, 1
The sum of a numbers and its positive square root is 6/25. Find the numbers.
There are three consecutive integers such that the square of the first increased by the product of the first increased by the product of the others the two gives 154. What are the integers?
Let us find two natural numbers which differ by 3 and whose squares have the sum 117.
Sum of the areas of two squares is 640 m2. If the difference of their perimeters is 64 m. Find the sides of the two squares.
Find two consecutive multiples of 3 whose product is 648.
Solve the following quadratic equations by factorization:
\[3\left( \frac{7x + 1}{5x - 3} \right) - 4\left( \frac{5x - 3}{7x + 1} \right) = 11; x \neq \frac{3}{5}, - \frac{1}{7}\]
Find the value of k for which the following equations have real and equal roots:
\[x^2 + k\left( 2x + k - 1 \right) + 2 = 0\]
If \[x^2 + k\left( 4x + k - 1 \right) + 2 = 0\] has equal roots, then k =
Solve the following equation: `(2"x")/("x" - 4) + (2"x" - 5)/("x" - 3) = 25/3`
Solve the following equation :
`1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6`
A two digit number is such that its product of its digit is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.
Solve the equation using the factorisation method:
`(3x -2)/(2x -3) = (3x - 8)/(x + 4)`
The side (in cm) of a triangle containing the right angle are 5x and 3x – 1. If the area of the triangle is 60 cm². Find the sides of the triangle.
Two pipes flowing together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.
Solve the following equation by factorization
`(2)/(3)x^2 - (1)/(3)x` = 1
If x4 – 5x2 + 4 = 0; the values of x are ______.
