Question

Present age of Asgar and Akbar is in the ratio 4:5. Ten years after, the

ratio of their ages will be 6:7. Find their present ages.​

Answer 1

Given :

• Present Age of Asgar and Akbar are in the ratio 4:5.
• After 10 years the ratio of thier ages will be 6:7.

To Find :

• Present Age of Asgar and Akbar.

Solution :

$\longmapsto\tt{Let\:Present\:Age\:of\:Asgar\:be=4x}$

$\longmapsto\tt{Let\:Present\:Age\:of\:Akbar=5x}$

After 10 years :

$\longmapsto\tt{Age\:of\:Asgar=4x+10}$

$\longmapsto\tt{Age\:of\:Akbar=5x+10}$

A.T.Q :

$\longmapsto\tt{\dfrac{4x+10}{5x+10}=\dfrac{6}{7}}$

$\longmapsto\tt{7(4x+10)=6(5x+10)}$

$\longmapsto\tt{28x+70=30x+60}$

$\longmapsto\tt{28x-30x=60-70}$

$\longmapsto\tt{-2x=-10}$

$\longmapsto\tt{x=\cancel\dfrac{-10}{-2}}$

$\longmapsto\tt\bold{x=5}$

Value of x is 5.

Therefore :

$\longmapsto\tt{Present\:Age\:of\:Asgar=4(5)}$

$\longmapsto\tt\bold{20\:yrs.}$

$\longmapsto\tt{Present\:Age\:of\:Akbar=5(5)}$

$\longmapsto\tt\bold{25\:yrs.}$

Answer 2

$\blue{\underline{\underline{{\large{\sf Given}}}}}$

• Present age of Asgar and Akbar is in the ratio 4 : 5
• Ten years after, the ratio of their ages will be 6 : 7

$\green{\underline{\underline{{\large{\sf To\:Find}}}}}$

• Their present ages

$\red{\underline{\underline{{\large{\sf Solution}}}}}$

• Let present age of Asgar be '4x'
• Let present age of Akbar be '5x'

★ After 10 years,

• Age of Asgar = 4x + 10
• Age of Akbar = 5x + 10

$\gray{\underline{\underline{{\large{\sf A.T.Q}}}}}$

$\implies$ (4x + 10)/(5x + 10) = 6/7

$\implies$ 7(4x + 10) = 6(5x + 10)

$\implies$ 28x + 70 = 30x + 60

$\implies$ 28x - 30x = 60 - 70

$\implies$ - 2x = - 10

$\implies$ x = - 10/- 2

$\implies$ x = 5

$\orange{\underline{\underline{{\large{\sf Therefore}}}}}$

• Present age of Asgar = 4(5) = 20 years
• Present age of Akbar = 5(5) = 25 years