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Q.

The students of a class are made to stand in(complete) rows. If one student is extra in row, there would be 2 rows less, and if one student is less in a row, there would be 3 rows more. Find the number of students in the class.


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a

28

b

30

c

60

d

20 

answer is C.

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Detailed Solution

Concept: By the given condition, we will find the total number of rows and the number of students in each row. Let the number of rows in which the students are lined are as x
and the number of students in each row as y, hence the total number of students becomes xy.
Let the number of rows in which the students are lined up = x
and, Let the number of students in each row = y
So, the total number of students =xy
Case 1:
Given, for each extra students in a row, there will be two rows less, so the number of rows =
 (x-2),
And, for the number of students in each row =y+1
So, the total number of students,
  ⇒xy=(x-2)(y+1)
  ⇒xy=xy+x-2y+(-2)
  ⇒x=2y-2……………………………………(i)
Case 2:
Given, for the each student less in a row, the number of rows =(x+3)
And, for the number of students in each row = y-1
So, the total number of students,
 ⇒xy=(x+3)(y-1)
  ⇒xy=xy-x+3y-3
  ⇒x=3y-3………………………………….(ii)
Now, on equating equation(i) and equation(ii), we get
⇒2y+2=3y-3
⇒2y-3y=-3-2
⇒-y=-5
⇒y=5
On putting the value of y in equation(i), we get
⇒x=2(5)+2
⇒x=12
As, the total number of students =xy
⇒xy=5×12
⇒xy=60
The total number of students is 60.
Hence, the correct answer is option 3.
 
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