Question

Present age of Anu and Raj are in ratio 4:5. Eight years from now the ratio of their ages will be 5:6. Find their present ages.​

Answer 1

Answer:

Let the present age of Anu and Raj be 4x

years and 5x respectively

After eight years, Anu age=(4x+8) years;

After eight years, Raj age=(5x+8) years.

Therefore,the ratio of their ages after eight years =(4x+8)

(5x+8)

This is given to be 5:6

Therefore,

4x+8 =5

5x+8 6

cross multiply gives

6(4x+8)=5(5x+8)

24x+48=25x+40

24x+48-40=25x

24x+8=25x

8=25x-25x

8=x

Therefore,Anu age=4x=4×8=32 years.

Raj age=5x=5×8=40 years.

Answer 2

Given : Present age of Anu and Raj are in the ratio 4:5 .Eight years later, the ratio of their ages will be 5:6 .

To Find : Find the Present age

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SolutioN : For Solving this type of Question let us form the Equation first .Than, we can solve it easily . Let's Solve :

$\maltese$ According to the Question :

$\longmapsto$ Present age of Anu and Raj are in the ratio 4:5 .So,

$\qquad \; \bigstar {\underline{\overline{\boxed{\pmb{\sf{ \bigg\{ \dfrac{Anu}{Raj} \bigg\} = \bigg\{ \dfrac{4y}{5y} \bigg\} }}}}}} \; \bigstar$

$\longmapsto$ After 8 years, the ratio of their ages will be 5:6 .So,

$\qquad \; \bigstar {\underline{\overline{\boxed{\pmb{\sf{ \bigg\{ \dfrac{4y + 8}{5y + 8} \bigg\} = \bigg\{ \dfrac{5}{6} \bigg\} }}}}}} \; \bigstar$

$\maltese$ Let's Cross Multiply :

${\dashrightarrow{\qquad{\sf{ \bigg\{ \dfrac{4y + 8}{5y + 8} \bigg\} = \bigg\{ \dfrac{5}{6} \bigg\} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 6 \bigg(4y + 8 \bigg) = 5 \bigg(5y + 8 \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 24y + 48 = 25y + 40 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 25y - 24y = 48 - 40 }}}} \\ \\ \\ \ {\qquad \; \; {\dashrightarrow{\underline{\boxed{\pmb{\frak{ y = 8 }}}}}}} \; {\red{\bigstar}}$

$\maltese$ Calculating the Present Age :

• Anu = 4y = 4(8) = 32 years
• Raj = 5y = 5(8) = 40 years

$\therefore \;$ Age of Anu is 32 years and age of Raj is 40 years .

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