The ages of two friends, Ram and Ravi, differ by 7 years and Ram is older than Ravi . Ram's mother Mayadevi is three times as old as Ram, and Ravi is four times as old as his brother Soham. The ages of Mayadevi and Soham differ by 65 years. Find the age of Mayadevi (in years).

The age difference between Ram and Ravi is 7 years.

Mayadevi's age is three times that of Ram.

Ravi's age is four times that of Soham.

The age difference between Mayadevi and Soham is 65 years. 

Solution:  

let the age of Ram be x, and Ravi's age be y.

According to the question:

x - y = 7 .... (1)

Mayadevi's age = 3x 

Soham age = $$\frac{y}{4}$$    

So, 

 $$3x -\frac{y}{4} = 65 \\ \implies = 12x -y = 260$$ ...... (2) 

Subtracting (1) and (2) . 

​$$12x-y=260 \\ \underline{-x + y= -7} \\ 11x = 253$$​​

x = 23 

Mayadevi's age = 3x = $$3 \times 23 = \bf69$$ years​