Question

10 year ago a was one third of cues is the ratio of the present ages of a and q is 4 is to 7 what is the total sum of their ages after 5 years

Answer 1

Answer:

Sum of age of $a$ and $q$ after 5 years is 54 years

Step-by-step explanation:

Let the present age of $a$ be 4x

Let the present age of $q$ be 7x

Age of $a$ 10 years ago $=4x - 10$ years

Age of $q$ 10 years ago $=7x - 10$ years

Given that 10 years ago, a was $\frac{1}{3}$ of q's age

$4x - 10 = \frac{1}{3} \times (\,7x - 10)\,\\\\ 3 \times (\,4x - 10)\, = 7x - 10\\\\ 12x - 30 = 7x - 10\\\\ 12x - 7x = -10 + 30\\\\ 5x = 20\\\\ x = 4$

Thus, present age of $a$ $= 4 \times 4 = 16\hspace{0.1cm}years$

Present age of $q$ $= 7 \times 4 = 28\hspace{0.1cm}years$

Age of $a$ after 5 years $=5 + 16 = 21\hspace{0.1cm}years$

Age of $q$ after 5 years $=5 + 28 = 33\hspace{0.1cm}years$

Thus, Sum of age of $a$ and $q$ after 5 years $= 21 + 33 = 54\hspace{0.1cm}years$