Shanna's age 10 years hence will be twice juhis present age.6 years back Shanna's age was 5/3 times juhis at that time find their present ages.
Answers
Application of linear equation.
Answer: present age of Juhi is 18 years and present age of Shanna is 26.
Explanation:
Given that Shanna's age 10 years hence means Shanna's age after 10 years will be twice Juhi's present age.
6 years back Shanna's age was 5/3 times Juihs age at that time.
lets assume present age of Juhi = x years
And present age of Shanna = y years
so Age of Shanna after 10 years will be present age of Shanna + 10
⇒ Age of Shanna after 10 years = y + 10
As given that Shanna's age after 10 years will be twice Juhi's present age.
⇒ Age of Shanna after 10 years = 2 × present age of Juhi
⇒ y + 10 = 2 × x
=> y = 2x - 10 ------------eq(1)
6 YEARS AGO
Age of Juhi 6 years ago = Present age of Juhi - 6 = x - 6
Age of Shanna 6 years ago = Present age of Shanna - 6 = y - 6
As 6 years back Shanna's age was 5/3 times Juihs age at that time.
⇒ Age of Shanna 6 years ago = 5/3( Age of Juhi 6 years ago )
⇒ y - 6 = 5/3 ( x - 6 )
⇒ 3y - 18 = 5x - 30
⇒3y - 5x = - 30 + 18
⇒3y - 5x = - 12 ----------eq(2)
Substituting y as 2x - 10 from eq(1) in eq(2) we get
3( 2x - 10) - 5x = -12
⇒6x - 30 - 5x = -12
⇒x = -12 + 30
⇒x = 18
On substituting x = 18 in eq (1) that is y = 2x - 10 we get
y = 2 × 18 - 10
⇒y = 36 - 10
⇒y = 26
Hence present age of Juhi = x = 18 years and present age of Shanna = y = 26years.
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