Question

Rs 500 were divided equally among a certain number of children.if there were 25 more children each would have received Rs 1 less fond the number of children

Answer 1

Given,

Total amount of money = Rs. 500

If there are 25 more children then each would have received Rs. 1 less than before.

To find,

The number of children.

Solution,

Let, the number of children = x

(Assume, x as a variable to do the further mathematical calculations.)

Each children will get = Rs. 500/x

According to the data mentioned in the question,

New number of children = x+25

Each children get = Rs. 500/(x+25)

Now,

500/(x+25) = 500/x -1

500/(x+25) = (500-x)/x

500x = 500x+12500-x²-25x

500x-500x+x²+25x = 12500

x²+25x= 12500

x²+25x-12500 = 0

x²+125x-100x-12500 = 0

x(x+125)-100(x+125) = 0

(x-100) (x+125) = 0

Either

(x-100) = 0

x = 100

Or,

x+125 = 0

x = -125

Now, number of children cannot be a negative number, so we will consider 100 as the value of x.

Hence, there are 100 children.