Rs. 7500 were divided equally among a certain number of children. Had there been 20 less children, each would have received Rs. 100 more. Find the original number of chlidren.
Answers
Let the original number of children be x
Money each child got = 7500/x
New number of children = x - 20
Money each child got = 7500 / (x-20)
7500 / (x-20) = 7500 / x + 100
7500 / (x-20) - 7500 / x = 100
( 7500x - 7500x + 150000 ) / ( x^2 - 20x ) = 100
150000 = 100 ( x^2 - 20x )
1500 = x^2 - 20x
x^2 - 20x - 1500 = 0
x^2 - 50x + 30x - 1500 = 0
x ( x - 50 ) + 30 ( x - 50 ) = 0
( x + 30 ) ( x - 50 ) = 0
Therefore, x = -30 or 50
Since number of children cannot be negative, -30 is rejected
Therefore, the original number of children = 50
Hope this helps you
Have a nice day :D
Answer:
hey mate.. here's ur answer..
Step-by-step explanation:
Total amt.to be distributed=₹7500
Let the original no.of children be 'x'..
therefore, initial share=7500/x
NOW 20CHILDREN ARE LESS..HERE..(as given in the question..)
so, no. of children will be..(x-20)
according to this..the new share =7500/x-20
GIVEN , THE DIFFERENCE IN SHARES=₹100
SO,BY QUESTION:
7500/x-20 - 7500/x =100
7500(x-20) - 7500x/(x-20)x =100
150000/x^2-20=100
150000=100x^2-2000x
x^2 -20x-1500=0
x^2-50x+30x-1500=0
(x-50) (x+30)=0
x=50 & x = -30.
BUT,
x =-30 is rejected because no.of children cannot be negative.
THEREFORE,x=50
HENCE , THE ORIGINAL NO.OF CHILDREN=50
HOPE IT HELPS YOU..FRND..
HAVE A GOOD DAY..