Correct Answer: ans: The number of children is 100 and amount of money 450 Tk.

Explanation:

Let, the number of children = x

and the amount of money each \gets = y Tk.

The total amount of money distributed = xy Tk.

so, According to question (x – 25) (y + 1.5) = xy……………………….. (i)

And (x+50) (y- l.5) =xy………………………… (ii)

We get from equation (i)

(x – 25) (y + 1.5) =xy

=> xy+ 1.5x – 25y-37.5 =xy

=> 1.5x – 25y = 37.5

=> 3x – 50y = 75 …………………(iii)

We get from equation (ii)

(x + 50) (y- l.5) =xy

=> xy-1.5x+50y-75 =xy

=> -1.5x + 50y = 75……………………….. (iv)

adding equation (iii) & (iv), we get

3x – 50y = 75

-1.5x + 50y = 75

1.5x =150

x = $\frac{150}{1.5}$ = 100

Putting the value of x in eqution (iii), we get

3x — 50y = 75

=> (3 x 100)-50y= 75

=> 300 – 50y = 75

=> – 50y = 75 – 300

=> – 50y = – 225

=> y=$\frac{-225}{-50}$

y = 4.5

Now putting the value of y in (iii)

=> 3x-50y = 75

=> 3x- (50) x (4.5) = 75

=>3x-225=75

=> 3x = 75 + 225

=> 3x = 300

=> x=$\frac{300}{3}$

x = 100

The number of children = x = 100 and

The total amount of money distributed = x $\times$ y = 4.5 x 100 = 450 Tk.