Four years ago, Shyam's age was $$\frac{3}{4}$$ times that of Ram. Four years hence, Shyam's age will be $$\frac{5}{6}$$ times that of Ram. What is the present age of Shyam?

Four years ago, Shyam's age was $$\frac{3}{4}$$ times that of Ram.

Let's assume four years ago, the age of Ram was 4y.

four years ago, the age of Shyam = $$\frac{3}{4}\times4y$$

= 3y

Four years hence, Shyam's age will be $$\frac{5}{6}$$ times that of Ram.

Four years hence, the ratio between the ages of Shyam and Ram will be 5:6 respectively.

$$\frac{3y+4+4}{4y+4+4}\ =\ \frac{5}{6}$$

$$\frac{3y+8}{4y+8}\ =\ \frac{5}{6}$$

$$\frac{3y+8}{2y+4}\ =\ \frac{5}{3}$$

9y+24 = 10y+20

10y-9y = 24-20

y = 4

The present age of Shyam = 3y+4

= $$3\times4+4$$

= 12+4

= 16 years