Question

If the ratio of the ages (in years) of x and y, 8 years ago is 7:6, then which of the following can be the
sum of their ages 8 years from now?
(A) 82
(B) 97
(C) 75
(D) 94​

Answer 1

Answer:

c) 75 is the correct answer.

Answer 2

Given,

Ratio of age of x and y, 8 years ago,

$\[\frac{x}{y} = \frac{7}{6}\]$

Solution,

Consider,

$\[\frac{x}{y} = \frac{{7k}}{{6k}}\]$

Sum of the age of x and y 8 years ago,

$\[\begin{array}{l} = x + y\\ = 7k + 6k\\ = 13k\end{array}\]$

Current sum of age,

$\[\begin{array}{l} = 13k + 8 + 8\\ = 13k + 16\end{array}\]$

Age after 8 years from now,

$\[\begin{array}{l} = 13k + 16 + \left( {8 + 8} \right)\\ = 13k + 32\end{array}\]$

Put different values of k to get the correct options.

$\[\begin{array}{l}k = 1,\\ = 13k + 32\\ = 13 \times 1 + 32\\ = 45\end{array}\]$

$\[\begin{array}{l}k = 2,\\ = 13k + 32\\ = 13 \times 2 + 32\\ = 58\end{array}\]$

$\[\begin{array}{l}k = 3,\\ = 13k + 32\\ = 13 \times 3 + 32\\ = 71\end{array}\]$

$\[\begin{array}{l}k = 4,\\ = 13k + 32\\ = 13 \times 4 + 32\\ = 84\end{array}\]$

$\[\begin{array}{l}k = 5,\\ = 13k + 32\\ = 13 \times 5 + 32\\ = 97\end{array}\]$

Hence the sum of age after 8 years is matching with given option (B).

The correct option is (B), i.e. 97