The sum of the ages of Farhan and his cousin is 38. Seven years ago, Farhan was thrice as old as he s cousin find his present age.
Answers
- The sum of the ages of Farhan and his cousin is 38.
- Seven years ago, Farhan was thrice as old as his cousin.
- Present age of Farhan
Let the present age of Farhan be x years.
Let the present age cousin be y years.
- The sum of the ages of Farhan and his cousin is 38.
Representing the condition mathematically to obtain our first equation.
=> x + y = 38 ----> 1
- Seven years ago, Farhan was thrice as old as his cousin.
Ages 7 years ago :-
Farhan = x - 7 years
Cousin = y - 7 years
Representing the second condition mathematically.
=> x - 7 = 3 ( y - 7)
=> x - 7 = 3y - 21
=> x - 3y = - 21 + 7
=> x - 3y = - 14 -----> 2
Multiply equation 1 by 3,
=> x + y = 38
=> 3 × x + 3 × y = 3 × 38
=> 3x + 3y = 114 ----> 3
Solve equations 3 and 2 simultaneously by elimination method.
Add equation 3 to equation 2,
3x + 3y = 114
x - 3y = - 14
---------------------
4x = 100
x =
Dividing by 2,
x =
x = 25
Substitute x = 25 in equation 3,
=> 3x + 3y = 114
=> 3 (25) + 3y = 114
=> 75 + 3y = 114
=> 3y = 114 - 75
=> 3y = 39
=> y =
=> y = 13
Farhan’s present age = 25 years
Correct question : The sum of the ages of farhan and his cousin is 38. Seven years ago, Farhan was thrice as old as his cousin. Find farhan’s present age.
Given :
- The sum of the ages of farhan and his cousin is 38.
- Seven years ago, Farhan was thrice as old as his cousin.
To find :
Farhan’s present age
Solution :
Step 1 of 2 :
Form the equation to find Farhan’s present age
Let Farhan’s present age = x years
It is given that the sum of the ages of farhan and his cousin is 38.
∴ Present age of Farhan’s cousin = (38 - x) years
Seven years ago
Farhan’s age = (x - 7) years
Age of Farhan’s cousin
= (38 - x - 7) years
= (31 - x) years
By the given condition
Step 2 of 2 :
Calculate Farhan’s present age
Farhan’s present age = 25 years
Present age of Farhan’s cousin
= (38 - 25) years
= 13 years
Hence , Farhan’s present age = 25 years
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