Question

On the playground, the students are asked to stand in rows with equal number of students in each row. If the students stand in lengths of
6,8,10 and 12 in each row,5 students are left out in each case. When they stand as 13 in a row, no student was left out. Find the total
number of students.​

Answer 1

Answer:

Let  the original number of rows =x

Let the original number of students in each row =y

Total number of students in class = Number of students ×  Number of rows =xy

According to problem

Case 1

Total no of students =(y+1)(x−2)=xy

⇒xy−2y+x−2=xy

 ⇒x−2y=2   ...(1)

Case 2

Case 2Total no of students =(y−1)(x+3)=xy

Case 2Total no of students =(y−1)(x+3)=xy⇒xy+3y−x−3=xy

Case 2Total no of students =(y−1)(x+3)=xy⇒xy+3y−x−3=xy ⇒x−3y=−3  ...(2)

Case 2Total no of students =(y−1)(x+3)=xy⇒xy+3y−x−3=xy ⇒x−3y=−3  ...(2)Subtracting eq(1) from eq(2) we get

Case 2Total no of students =(y−1)(x+3)=xy⇒xy+3y−x−3=xy ⇒x−3y=−3  ...(2)Subtracting eq(1) from eq(2) we get−y=−5

Case 2Total no of students =(y−1)(x+3)=xy⇒xy+3y−x−3=xy ⇒x−3y=−3  ...(2)Subtracting eq(1) from eq(2) we get−y=−5⇒y=5

Case 2Total no of students =(y−1)(x+3)=xy⇒xy+3y−x−3=xy ⇒x−3y=−3  ...(2)Subtracting eq(1) from eq(2) we get−y=−5⇒y=5Putting the value of y in eq(1)

Case 2Total no of students =(y−1)(x+3)=xy⇒xy+3y−x−3=xy ⇒x−3y=−3  ...(2)Subtracting eq(1) from eq(2) we get−y=−5⇒y=5Putting the value of y in eq(1)x−2(5)=2

Case 2Total no of students =(y−1)(x+3)=xy⇒xy+3y−x−3=xy ⇒x−3y=−3  ...(2)Subtracting eq(1) from eq(2) we get−y=−5⇒y=5Putting the value of y in eq(1)x−2(5)=2⇒x=12

Case 2Total no of students =(y−1)(x+3)=xy⇒xy+3y−x−3=xy ⇒x−3y=−3  ...(2)Subtracting eq(1) from eq(2) we get−y=−5⇒y=5Putting the value of y in eq(1)x−2(5)=2⇒x=12Hence we get x=12 and y=5

Case 2Total no of students =(y−1)(x+3)=xy⇒xy+3y−x−3=xy ⇒x−3y=−3  ...(2)Subtracting eq(1) from eq(2) we get−y=−5⇒y=5Putting the value of y in eq(1)x−2(5)=2⇒x=12Hence we get x=12 and y=5Total no. of students =xy=60

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