Students of a school were to stand in row for drill. If 3 students less were standing in each row. 10 more rows were required & if 5 students more were standing in each row then the number of rows were reduced by 10. Find the number of students.
Answers
Answered by
5
Step-by-step explanation:
Let the number of rows be x and the number of students in a row be y.
So, the total number of students = xy.
(i)
3 students less were standing in each row. 10 more rows were required.
⇒ (y - 3)(x + 10) = xy
⇒ xy + 10y - 3x - 30 = xy
⇒ -3x + 10y = 30
⇒ 3x - 10y = -30 ------ (1)
(ii)
Given, 5 more students were standing then the numbers of rows were reduced by 10.
⇒ (y + 5)(x - 10) = xy
⇒ xy - 10y + 5x - 50 = xy
⇒ 5x - 10y = 50 ------ (2)
On solving (1) & (2), we get
⇒ 3x - 10y = -30
⇒ 5x - 10y = 50
-------------------
-2x = -80
x = 40.
Substitute x = 40 in (1), we get
⇒ 3x - 10y = -30
⇒ 3(40) - 10y = -30
⇒ 120 - 10y = -30
⇒ -10y = -30 - 120
⇒ y = 15.
Therefore, number of students = xy = 600.
Hope this helps!
Similar questions