Answer:
Age of son = 6 years
Age of man = 5×6 = 30 years
Step-by-step explanation:
<u>GIVEN :-</u>
- A man is 5 times as old as his son. (In Present)
- 4 years ago , the man was 13 times as old as his son
<u>TO FIND :-</u>
- The present ages of the man & his son.
<u>SOLUTION :-</u>
Let the present age of son be 'x'.
⇒ Present age of man = 5x
4 years ago ,
Age of son = (Present age of son) - 4 = x - 4
Age of man = (Present age of man) - 4 = 5x - 4
The man was thirteen times as old as his son. So,
![=> 5x - 4 = 13(x - 4)](https://tex.z-dn.net/?f=%3D%3E%205x%20-%204%20%3D%2013%28x%20-%204%29)
Now , solve the equation.
- Open the brackets in R.H.S.
![=> 5x - 4 = 13x - 52](https://tex.z-dn.net/?f=%3D%3E%205x%20-%204%20%3D%2013x%20-%2052)
- Take 5x to R.H.S. and -52 to L.H.S. Also , take care of their signs because they are getting displaced from L.H.S. to R.H.S. or vice-versa.
![=> 13x - 5x = 52 - 4](https://tex.z-dn.net/?f=%3D%3E%2013x%20-%205x%20%3D%2052%20-%204)
![=> 8x = 48](https://tex.z-dn.net/?f=%3D%3E%208x%20%3D%2048)
- Divide both the sides by 8
![=> \frac{8x}{8} = \frac{48}{8}](https://tex.z-dn.net/?f=%3D%3E%20%5Cfrac%7B8x%7D%7B8%7D%20%3D%20%5Cfrac%7B48%7D%7B8%7D)
![=> x = 6](https://tex.z-dn.net/?f=%3D%3E%20x%20%3D%206)
<u>CONCLUSION :-</u>
Age of son = 6 years
Age of man = 5×6 = 30 years