Question

The sum of ages of A and B is now 110 years and their ages 20 years ago were in the
ratio 4 : 3. What is the age of A?

Answer 1

we know that,
A + B=110
But 20 years ago,
A-20 + B-20 = 110-40
So we can say that,
A-20 + B-20 =4:3
and let the common multiple for 4:3 be x
4x +3x=110-40
7x =70
x =70/7
x =10
so,
4x=4*10=40=A-20
so,
40=A-20
60=A

Answer 2

Let the ages of A and B now are X and Y
X + Y =110
3X+3Y = 330
$\frac{X-20}{Y-20}$ = $\frac{4}{3}$
3X - 60 = 4Y - 80
3X - 4Y = - 20

3X+3Y = 330
3X - 4Y = - 20
--------------------
7Y = 350
Y = 50