The Distribution in Charity

Suppose that Sanya distributes money beween $x$ people. Then Vibha distributes money between $x+5$ people. Assuming that it's meant that each of them distributes the charity evenly, we can use the second part to get: $\frac{100}{x+5}+1=\frac{100}{x}$ Comming to a common denumerator we get $x^2+5x=500$ ,i.e $x^2+5x-500=(x+25)(x-20)=0$ .

As, clearly, $x>0$ , we get $x=20$ . So Sanya gives charity to $20$ people and hence Vibha gives charity to $25$ people. In total, the number of recipients of the charity is $20+25=\boxed{45}$

V»x+5,y-1 S»x,y (where x is the number of people Sanya gives money, y is the number of rupees she gives each) thus for V»100=(x+5)(y-1) S»100=xy . Solving for x gives 20 or -25 , thus Sanya donated to 20 people and Vibha gave to 25 people (20+5), therefore total number of people donated to is 45.