Question

Anu is 24 years elder to Monali. The respective ratio between Anu's age four
years from now and Monali's age at the same time will be 11: 3. What was Anu's
age four years ago ? in years)​

Answer 1

AnswEr :

• Anu is 24 years elder to Monali.
• Four years from now, Ratio of age will be 11 : 3
• Anu's age four years ago will be?

• According to the Question :

⇒ Anu is 24 years elder to Monali

⇒ Anu = Monali + 24

⇒ A = M + 24 ⠀⠀⠀⠀⠀—eq.( I )

_______________________________

• F O U R ⠀Y E A R S ⠀F R O M ⠀N O W :

↠ Anu : Monali = 11 : 3

↠ (A + 4) : (M + 4) = 11 : 3

• Putting value of A from eq.( I )

↠ (M + 4 + 24) : (M + 4) = 11 : 3

↠ (M + 28) : (M + 4) = 11 : 3

• Product of Extreme = Product of Mean

↠ 3 × (M + 28) = 11 × (M + 4)

↠ 3M + 84 = 11M + 44

↠ 84 – 44 = 11M – 3M

↠ 40 = 8M

• Dividing both term by 8

↠ M = 5 years

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• P R E S E N T ⠀A G E S :

◗ Anu = M + 24 = (5 + 24) = 29 years

◗ Monali = M = 5 years

━━━━━━━━━━━━━━━

• Four Years Ago ( Past ) :

↦ Anu = Present – 4 = (29 – 4) = 25 years

↦ Monali = Present – 4 = (5 – 4) = 1 year

∴ Anu's age four years ago was 25 years.

#answerwithquality #BAL

Answer 2

$\bf{\Huge{\underline{\boxed{\sf{\green{ANSWER\::}}}}}}$

$\bf{\Large{\underline{\bf{Given\::}}}}$

Anu is 24 years elder to Monali. The respective ratio between Anu's age four years from now & Monali's age at the same time will be 11:3.

$\bf{\Large{\underline{\bf{To\:find\::}}}}$

Anu's age was four years ago.(In years)

$\bf{\Large{\underline{\boxed{\sf{\pink{Explanation\::}}}}}}$

Let the Monali's age be R years.

Let the Anu's age be R + 24 years.

A/q

• $\bf{\large{\underline{\boxed{\sf{\blue{After \:4\:years\::}}}}}}$

$\sf{The\:Monali\:age\:=\:(R+4)\:years}$

$\sf{The\:Anu's\:age\:=\:(R+4+24)\:years}$

Therefore,

$\longmapsto\rm{Anu:Monali=11:3}$

$\longmapsto\rm{(R+4+24):(R+4)\:=\:(11:3)}$

$\longmapsto\rm{\frac{R+4+24}{R+4} =\frac{11}{3} }$

$\longmapsto\rm{\frac{R+28}{R+4} =\frac{11}{3} }$

$\bf{\large{\underline{\sf{\orange{Cross\:Multiplication\::}}}}}}$

$\longmapsto\rm{3(R+28)\:=\:11(R+4)}$

$\longmapsto\rm{3R+84\:=\:11R+44}$

$\longmapsto\rm{3R\:-\:11R\:=\:44\:-\:84}$

$\longmapsto\rm{\:-8R\:=\:-40}$

$\longmapsto\rm{R\:=\:\cancel{\frac{-40}{-8} }}$

$\longmapsto\rm{\red{R\:=\:5\:years}}$

Now,

The present age of Monali's = 5 years.

The present age of Anu's = (24 + 5) = 29 years.

• $\bf{\Large{\underline{\boxed{\sf{\blue{4\:years\:ago\::}}}}}}$

The Monali's age = (5 - 4) years = 1 years.

The Anu's age = (29 - 4) years = 25 years.

Thus,

$\bf{\large{\boxed{\rm{\purple{Four\:years\:ago\:the \:age\:of\:Anu's\:was\:25\:years}}}}}}$