6 times the present age of Sujatha is 6 years more than 3 times the present age of Vanita. After 7 years, 4 times the age of Vanita will be 6 years less than 6 times the age of Sujatha. The age of Vanita is k years more than that of Sujatha. What is the value of k?​

Correct option is B

Given:

Let the present age of Sujatha be S years.
Let the present age of Vanita be V years.

Concept Used:

Translate the given statements into algebraic equations to solve for the values of S and V.

Solution:

Translate the first condition into an equation:
We are given that 6 times the present age of Sujatha is 6 years more than 3 times the present age of Vanita.
This can be written as:
6S = 3V + 6 (Equation 1)
Translate the second condition into an equation:
After 7 years, 4 times the age of Vanita will be 6 years less than 6 times the age of Sujatha.
This can be written as:
4(V + 7) = 6(S + 7) - 6 (Equation 2)
Simplify Equation 2:
Expand both sides:
4V + 28 = 6S + 42 - 6
4V + 28 = 6S + 36
Now, subtract 28 from both sides:
4V = 6S + 8 (Equation 3)
Solve the system of equations:
Now, we have two equations:
6S = 3V + 6
4V = 6S + 8
Substitute 6S = 3V + 6 from Equation 1 into Equation 3:
4V = (3V + 6) + 8
4V = 3V + 14
Now subtract 3V from both sides:
V = 14
Find the age of Sujatha:
Now that we know V = 14, substitute this value into Equation 1 to find S:
6S = 3(14) + 6
6S = 42 + 6
6S = 48
S = 8
Find the value of k:
The age of Vanita is V = 14, and the age of Sujatha is S = 8.
The value of k, which is the difference in their ages, is:
k = V - S = 14 - 8 = 6