Question

The ratio of the present ages of sunita and Vinita is 4:5. Six years hence, the ratio of their ages will be 14:17. What will be the ratio of their ages 12 years hence?
A. 16:19
B. 17:19
C. 15:19
D. 13:15

Answer 1

Hint: We have been given with the ratio of the ages of sunita and Vinita presently and after six years. To solve this we will have to make certain assumptions. Since we have to calculate the ratio of ages for both of them after 12 years.
Let the present age of sunita be= $ 4x $ years
Let the present age of vinita be= $ 5y $ years
Since we are given with their ratios we will multiply the ratio with the assumed variable.

Complete step-by-step answer:
According to the conditions in the given question after six years ratio of their ages will be
 $ \dfrac{{4x + 6}}{{5x + 6}} = \dfrac{{14}}{{17}} $
Cross multiplying we get,
 $
\Rightarrow 17(4x + 6) = 14(5x + 6) \\
\Rightarrow 68x + 102 = 70x + 84 \;
 $
Grouping the variables at one side and all the constants at another side
 $
\Rightarrow 102 - 84 = 70x - 68x \\
\Rightarrow 18 = 2x \\
  x = 9 years \;
 $
Therefore substituting the value in the ratio we get the present age of sunita= $ 4 \times 9 = 36 years $ and the present age of Vinita is = $ 5 \times 9 = 45 years $
After 12 years
The age of sunita will be = $ 36 + 12 = 48 \text years $
The age of Vinita will be = $ 45 + 12 = 57 \text years $
Ratios of their ages after 12 years will be 48:57
Now dividing by 3 we get the ratio as 16:19. Hence the correct option is A.
So, the correct answer is “Option A”.

Note: The above question involves the concept of linear equation in two variables and we know that though every linear equation in one variable has a unique solution but we cannot say about the solution of linear equation involving two variables. In this equation there are two variables. A solution contains one value for x and another value for y which satisfy the given equation.