Question

A sum of money was distributed equally among a certain no of children.if there were 10children more,each would get a rupee less.but if there were 15children less each would get of ₹3 more.

Answer 1

let the no of students be X and the amount given to each student be Y
therefore total amount distributed is xy
from the first condition we get
(X + 10)(Y-1)=XY
XY-X+10Y-10=XY
-X+10Y=10 eqaution 1

from the second condition we get
(X-15)(Y+3)=XY
XY+3X-15Y-45=XY
3X-15Y=45
X-5Y=15 DIVIDE BY 3 eqaution 2


adding eqaution 1 and 2
-X+10Y=10
X-5Y=15

5Y=25
Y=5
substituting the value of Y in equation 1
we get
-X+10Y=10
-X+10*5=10
-X+50=10
-X=10-50
-X=-40
X=40

there are 40.STUDENTS and the total amount is 200 rupees