Students of a school were made to stand in rows for drill. If 3 students less were standing in each rows , 10more rows were required and if 5 students more were standing in each row then the number of rows was reduced by 10 Find the number of students participating in the drill ?
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Answers
Answer:
Step-by-step explanation:
Let the number of rows be x and number of students in each row be y
Then total students will be=x*y
Now according to question
(x+10)(y-3)=xy
xy-3x+10y-30=xy
10y-3x=30-----------------(eq1)
Now..
(x-10)(y+5)=xy
xy+5x-10y-50=xy
5x-10y=50 ---------------(eq 2)
Adding eq 1 and 2 we get
2x=80
x=40
Putting x=40 in eq 1 we get
10y-120=30
10y=150
y=15
total no=x*y=600
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!