students of a school were were made to stand in rows for drill. if 3 students less were standing in each row, 10 more rows were required and if 5 students
Answers
Let the students in each rows be x and student ome row be y.
Hence,Total student=xy.
from 1st case,
(x-3)(y+10)=xy
x(y+10)-3( y+10)=xy
xy+10x-3y-30=xy
10x-3y=30 ..................(i)
From 2nd case
(x+5)(y-10)=xy
x(y-10)+5(y-10)=xy
xy-10x+5y-50=xy
-10x+5y=50. .....................(ii)
Let's adding (i) & (ii)
10x-3y=30 2y = 80
-10x+5y=50 y=80÷2
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2y = 80 So, y=40.
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put y=40 in euation (i)
10x-3y=30
10x-3×40=30
10x-120=30
10x=30+120
10x=150
x=150/10
so,x=15
Total student= xy=15×40=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
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-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!