Math, asked by SusanAabidi2680, 10 months ago

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

Answered by ShreyaSingh31
54

\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}}}}}}

Answered by pulakmath007
3

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

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If p- 5 gives 12 then p is _____

https://brainly.in/question/22500317

2. A number when subtracted from 40 results into 15. This statement in the form of an equation

https://brainly.in/question/25043268

#SPJ3

Similar questions