Question

The present ages of Mary and Joseph are in the ratio 5:3. After 3 years sum of their ages will be
38. Find their present ages.
​

Answer 1

Given,

Ratio of age of Mary and Joseph $\[ = 5:3\]$

Sum of age after three years $\[ = 38\]$

Solution,

Consider the present age of Mary and joseph is m and j.

$\[\frac{m}{j} = \frac{3}{2} - - - - - \left( 1 \right)\]$

$\[\begin{array}{l}\left( {m + 3} \right) + \left( {j + 3} \right) = 38\\ \Rightarrow m + j = 32 - - - - \left( 2 \right)\end{array}\]$

Put the value of m from equation 1 to 2,

$\[m + j = 32\]$

$\[ \Rightarrow \frac{3}{2}j + j = 32\]$

$\[ \Rightarrow \frac{5}{2}j = 32\]$

$\[ \Rightarrow j = \frac{{64}}{5}\]$

Calculate the value of m from equation 1,

$\[\begin{array}{l}m = \frac{3}{2}j\\ \Rightarrow m = \frac{3}{2} \times \frac{{64}}{5}\\ \Rightarrow m = \frac{{96}}{5}\end{array}\]$

Hence the present age of Mary and Joseph is $\[\frac{{96}}{5}years\]$ and $\[\frac{{64}}{5}years\]$.