A teacher on attempting to arrange the students for mass drill in the form of a solid square found t

M4maths Previous Puzzles

21 Aug 2013 A teacher

A teacher on attempting to arrange the students for mass drill in the form of a solid square found that 24 students were left over. 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.

OPtion

1) 450
2) 470
3) 495
4) 525
5) 550
6) 600
7) 700
8) 1200
9) 2400
10) None of these

Solution

Let the number of students in one side = x
Total number of students = x^2+24 (because 24 students were left)
When size of the square in increased by 1
then total number of students = (x+1)^2 - 25 (25 students were short)
Now the number of students in same,
x^2 + 24 = (x+1)^2 - 25
solve
x = 24
Total number of students = 24^2 + 24 = 600
option 6

Correct Option: 6 Best Solution (22)

FRANKLIN VIJAY   11 years AGO

no of students be x
side of square be y
y*y=x-24 => y^2=x-24 =>1st equation
(y+1)(y+1) = x + 25 =>2nd equation
y^2+2y+1=x+25
on substituting 1st equation we get
x-24+2y+1=x+25
we get 2y=48
so=>y = 24
on subst y=24 in 2nd equation
25*25=x+25
x=625-25
x = 600
no of studnts= 600

Like? Yes (20) | No (6)  

Muhammad Nadeem Haider Naseem   11 years AGO

Let the side of the square be x.
No. of students = x
2
+ 24
New side = x + 1
No. of students = (x + 1)2
– 25
APQ ⇒ x
2
+ 24 = (x + 1)2 – 25
⇒ x
2
+ 24 = x
2
+ 2 x + 1 - 25
⇒ 2x = 48
⇒ x = 24
∴ side of square = 24
No. of students = 576 + 24
= 600

Like? Yes (10) | No (4)  

nishant kumar   11 years AGO

let the no. of students be ---- x
the side of the square be ----- y
y*y = x - 24
(y+1)(y+1) = x + 25
on solving them simultaneously.....we have y = 24
x = 600
Total students = 600
ANS: 600 students.

Like? Yes (7) | No (3)  

Mayuresh Srivastava   11 years AGO

Let the no. of students be ---- a
the side of the square be ---- x
x*x=a-24
(x+1)(x+1)=a+25
on solving we have x = 24 a = 600
Total students = 600.

Like? Yes (7) | No (3)  

kishor kumar   11 years AGO

let side of square = x
so no. of st. = x^2+24
now if side of squar increased by 1
than no of student = (x+1)^2-25
becoz no of students are equal in both cases so
x^2+24 = (x+1)^2-25
or x = 24
so no of st. = (24)^2+24 =600

Like? Yes (6) | No (2)  

krishnapriya   11 years AGO

let the no of students be 'x'
the side of square be 'y'
given, y*y=x-24--------(1)
(y+1)(y+1)=x+25--------(2)
solving the equations (1) and (2) we get
x=600 and y=24

Like? Yes (5) | No (2)  

mohan lal garg   11 years AGO

Let no of students be x

& side of square be y

then y *y = x - 24

according to other condition ( y + 1 ) ( y + 1 ) = x + 25

on solving them we get y = 24 and the value of x = 600

therefore no of students are 600 and value of each side of square is 24

Like? Yes (5) | No (2)  

Vinay Sipani    11 years AGO

Let No. of students on each side = x
Arranging students in form of solid square
No of students in square = area = x^2
=> Total no. of students = x^2 + 24

Increasing 1 student on each side
=> No of students in square = area = (x + 1)^2
But 25 students were less
=> Total no of students = (x + 1)^2 - 25

=> x^2 + 24 = (x + 1)^2 - 25
=> 49 = 2x + 1
=> x = 24
=> No. of students = x^2 + 24 = 600

Like? Yes (5) | No (2)  

Anil Kumar Bharti   11 years AGO

Exp:
let the no. of students be ---- x
the side of the square be ----- y
y*y = x - 24
(y+1)(y+1) = x + 25
on solving them simultaneously.....we have y = 24
x = 600
Tot stu = 600 Ans

Like? Yes (6) | No (3)  

Amit kumar   11 years AGO

let the no. of students is x
the side of the square is y
according to ques
y*y = x - 24
(y+1)(y+1) = x + 25
on solving the equations we have y = 24
x = 600
Total students = 600
ANS: 600 students.

Like? Yes (4) | No (2)  

P.L.ANANTHI   11 years AGO

let the side of the square be x m
students be y
1 case
y = x2 + 24---1
2nd case
y = (x + 1) square - 25-------------2
from eq 1 and eq 2
x2 +24 = x + 1 square -25
x = 24
puttin in eq 1
y = 600

Like? Yes (2) | No   

Niraj   11 years AGO

Let no of students be x & side of square be y
then according to given conditions
y*y=x-24 ----------- (1)
(y+1)(y+1)=x+25 ----------- (2)
on solving these 2 equations,
x=600 and y=24
So no of students are 600 and each side of square is 24

Like? Yes (4) | No (2)  

MOVVA ROHITH   11 years AGO

let there are total y students
and in square there is x rows and x columns
so,x^2=y-24 from the 1st condition
and (x+1)^2=y+25 from 2nd condition.
by solving these two we get y=600.

Like? Yes (3) | No (2)  

Md.Sultan Khichi   11 years AGO

let the total no. of students be y and side of the square be x.
according to the ques
x^2=y-24
(x+1)^2=y+25
after solving this x=24.
y=24^2+24=600.
total no of students are 600.
Ans:6.

Like? Yes (3) | No (2)  

deepak kumar   11 years AGO

total no. of students => x^2+24=(x+1)^2-25
solving this we get x=24
so total no. of students =24^2+24=(25)^2-25=600

Like? Yes (1) | No   

SHIVANI PRAKASH   11 years AGO

let initially the square formed was with x students on each side and 24 were left.
thus total students=x^2+24
the side of square was increased by 1 and 25 students were short.
thus total students=(x+1)^2-25
x^2+24=(x+1)^2-25
thus x=24
and x^2+24=600 is the required answer...

Like? Yes (3) | No (2)  

aman kumar tiwari   11 years AGO

let the no. of students be ---- x
the side of the square be ----- y
y*y = x - 24
(y+1)(y+1) = x + 25
on solving them simultaneously.....we have y = 24
x = 600
Total students = 600
ANS: 600 students.

Like? Yes (1) | No   

Devendra Marghade   11 years AGO

If number of student=x and
student to be arranged in a line=n
Ist case:n^2+24=x or n^2=x-24 ---(i) &
IInd case:(n+1)^2=x+25 or n^2+2n+1=x+25 ---(ii)
Substituting value of n^2 in (ii),
(x-24)+2n+1=x+25, n=24,so x=n^2+24=24^2+24=600

Like? Yes (2) | No (2)  

Bingumalla Abinay   11 years AGO

x^2+24=(X+1)^2-25
solving we get x=24
total no students = X^2+24=600

Like? Yes (2) | No (2)  

IFFAT IRAM   11 years AGO

let the no. of students in a row be x
total no. of students forming a square= x^2
overall students=x^2+24
new no. of students forming a square= (x+1)^2
overall student=(x+1)^2-25

x^2+24=(x+1)^2-25
x^2+24=x^2 +1+2x-25
24=2x-24
2x=48
x=24

no. of students x^2+24
=> 24^2+24
600

Like? Yes (2) | No (2)  

siddanth   11 years AGO

x^2 + 24 = (x+1)^2-25

=> x=24
no of students x^2+24 = 600

Like? Yes (2) | No (2)  

Eliza    11 years AGO

let x be the total number of students. Let y be the number of students arranged in each row and column of the square. Hence there will be y^2 students arranged in the form of square.
also x-(y^2)=24 --> x= 24+y^2
(y+1)^2-x=25
(y^2)+2y+1-(y^2)-24=25
2y=48
y=24
hence x=576+24=600

Like? Yes (2) | No (2)