Question

A and B both the have some pencils. If A gives 10 pencils to B, then B will have twice as many as A. And if B gives 10 pencils to A, then they will have the same number of pencils. How many pencils does each have ?

Answer 1

Let the numberof pencils with A = x
and the number of pencils with B = y.

If A gives 10 pencils to B,
y + 10 = 2( x - 10 )
2x - y = 30                                    ...(1)

If B gives to pencils to A
y - 10 = x + 10 
x - y = - 20                                   ...(2)

Subtracting equation (1) and (2),
     x  -  y = - 20 
-   2x - y = 30    
     - x = - 50
        x = 50

From (1)
2(50) - y = 30
y = 70
Thus, A has 50 pencils and B has 70 pencils.