2 times the present age of Urvashi is 6 years more than the present age of Ayushi. The present age of Mohan is 4 times the present age of Urvashi, and Ayushi is 8 years younger than Sanju. If the sum of the present ages of Mohan and Sanju is 50 years, then Urvashi's present age (in years) is:​

Correct option is A

Given:

Mohan is 4 times Urvashi

Ayushi is 8 years younger than Sanju

2 times Urvashi is 6 more than Ayushi

Sum of Mohan and Sanju's ages is 50

Solution:

​Let the present ages be:

Urvashi = x years

Ayushi = y years

Mohan = 4x years 

Sanju = y + 8 years 

Now, 

2x = y + 6

2x - y = 6  .......(1)

and 

4x + y + 8 = 50

4x + y = 42 .......(2)

From (2) - 2(1) and 

​$$4x +y =42 \\ \underline{-4x \mp2y=-12}\\ 3y \quad =\quad 30 \\ \ \\ y=10$$​​

Substituting y = 10 in (1) 

2x - 10 = 6 

2x = 10 + 6 = 16 

x = 8 

Thus, Urvashi's present age is 8 years.