Q.10 Aman's age is three times his son's age .Ten years ago he was five times his son 's age.Find their present ages.
Answers
Answer:
The present age of Aman is 60 years and his son is 20 years.
Step-by-step explanation:
Given :
Aman's age is three times his son's age. Ten years ago, he was five times his son's age.
To find :
their present ages
Solution :
Let the present age of Aman's son be x years.
Aman's age is three times his son's age.
So, Aman's present age = 3x years
Ten years ago,
Aman's age = (3x – 10) years
His son's age = (x – 10) years
According to the question,
3x – 10 = 5(x – 10)
3x – 10 = 5x – 50
5x – 3x = 50 – 10
2x = 40
x = 40/2
x = 20
Therefore, the present age of Aman's son is 20 years.
Aman's age :
= 3(20)
= 60 years
The present age of Aman is 60 years.
Given information
- ↠Aman's age is three times his son's age .
- ↠Ten years ago he was five times his son's age .
What we have to calculate
- ↠ We have to calculate their present ages .
How we calculate
- ↠ Assume a variable (unknown) eg: x or y
- ↠ According to the given statement setup the equation in terms of x or y
- ↠ Solve the equation
- ↠After that put the value of x or y
Let's us assume
- ↠ Let's Aman's son age be y years
Finding out their present age
❍As given the Aman's age is three times his son's age
Therefore
- ↠Aman's present age = 3 × x
- ↠Aman's present age = 3x years
Ten years ago
- Aman's age = ( 3x -10)
- And his son age = ( x -10)
Forming an equation
❑ Aman's age equal five times his son age
- ↠ (3x - 10) = (x -10)
Solving equation
↬ Aman's age = five times his son age
- Submitting values
↬ (3x -10) =5 ( x - 10)
- Opening bracket
↬ 3x - 10 = 5x - 50
- Transferring sides
↬ 3x - 5x = 10 - 50
- On subtracting
↬ 2x = 40
- Transferring sides
↬ x = 40/2
- On Dividing 40 by 2
↬ x = 20
The present age of Aman's son is 20 years
Now we find Present age of Aman's
↬Aman's present age = 3x
- Submitting values
↬Aman's present age = 3 × 20
- On multiplying
↬ Aman's present age = 60