Question

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.

Answer 1

$\bf{\huge{\underline{\boxed{\sf{\red{Answer:}}}}}}$

$\bf{\underline{\underline{\sf{\green{Given}}}}}$

• The sum of the ages of Farhan and his cousin is 38.
• Seven years ago, Farhan was thrice as old as his cousin.

$\bf{\underline{\underline{\sf{\green{To\:find}}}}}$

• Present age of Farhan

$\bf{\underline{\underline{\sf{\green{Solution}}}}}$

Let the present age of Farhan be x years.

Let the present age cousin be y years.

$\bf{\underline{\underline{\sf{\green{As\:per\:first\:condition}}}}}$

• 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

$\bf{\underline{\underline{\sf{\green{As\:per\:second\:condition}}}}}$

• 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 = $\large\frac{100}{4}$

Dividing by 2,

x = $\large\frac{50}{2}$

x = 25

Substitute x = 25 in equation 3,

=> 3x + 3y = 114

=> 3 (25) + 3y = 114

=> 75 + 3y = 114

=> 3y = 114 - 75

=> 3y = 39

=> y = $\large\frac{3}{39}$

=> y = 13

$\bf{\large{\underline{\boxed{\sf{\pink{Present\:age\:of\:Farhan\:=\:x\:=\:25\:years}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\pink{Present\:age\:of\:cousin\:=\:y\:=\:13\:years}}}}}}$

Answer 2

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

$\displaystyle \sf (x - 7) = 3(31 - x)$

Step 2 of 2 :

Calculate Farhan’s present age

$\displaystyle \sf (x - 7) = 3(31 - x)$

$\displaystyle \sf{ \implies }x - 7 = 93 - 3x$

$\displaystyle \sf{ \implies }x + 3x = 93 + 7$

$\displaystyle \sf{ \implies }4x = 100$

$\displaystyle \sf{ \implies }x = \frac{100}{4}$

$\displaystyle \sf{ \implies }x = 25$

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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