Question

the ages of Asha and Sushma are in ratio 7:2 . Eight year hence , the ratio of their ages will be 5:2 . Find the present age.​

Answer 1

Answer:

$\large\mathbf\color{green}\underline{\underline{Question:}}$

$\textsf{The ages of Asha and Sushma are in ratio 7:2.}$

$\textsf{Eight year hence , the ratio of their ages will}$

$\textsf{be 5:2 . Find the present age.}$

$\large\mathbf\color{blue}\underline{\underline{Given:}}$

$\textsf{Present ratio of the ages of Asha and Shusma = 7:2}$

$\textsf{Ratio of their ages after 8 years = 5:2}$

$\large\mathbf\color{orange}\underline{\underline{To\:find:}}$

$\textsf{Find their present age}$

$\large\mathbf\color{magenta}\underline{\underline{Taken:}}$

$\textsf{Let the age of Asha and Sushma be 7x and 2x}$

$\textsf{Age of Asha will be}$

$\mapsto{7x+8}$

$\textsf{Age of Sushma will be}$

$\mapsto{2x+8}$

$\textsf{To find both ages we have to use this equation}$

$\mapsto{(7x+8)/(2x+8)=5:2}$

$\large\mathbf\color{purple}\underline{\underline{Concept:}}$

$\textsf{▪︎Apply formula of cross multiplication}$

$\textsf{▪︎Then subtract and divide}$

$\textsf{▪︎Now multiply with the ratio 7:2}$

$\large\mathbf\color{pink}\underline{\underline{Solution:}}$

$\textsf{(7x+8)/(2x+8)=5:2}$

$\Rightarrow{2(7x+8)=5(2x+8)}$

$\textsf{Use cross multiplication}$

$\Rightarrow{14x+40=10x+16}$

$\Rightarrow{14x-10x=40-16}$

$\Rightarrow{4x=24}$

$\Rightarrow{x=24/4}$

$\therefore\boxed{x=6}$

${\purple{\boxed{\underline{Age\:of\:Asha=6×7=42years}}}}$

${\purple{\boxed{\underline{Age\:of\:Sushma=6×2=12years}}}}$

_______________________________________

So , the age of Asha and Sushma is 42 years and 12 years respectively....

BE BRAINLY

Answer 2

✬ Asha = 42 years ✬

✬ Sushma = 12 years ✬

Step-by-step explanation:

Given:

• Ages of Asha and Sushma are in ratio 7 : 2.
• After 8 years their ages will be in ratio of 5 : 2.

To Find:

• What are their present ages ?

Solution: Let x be the common in given ratio. Therefore,

➟ Asha's age = 7x years

➟ Sushma's age = 2x years

[ Eight years hence their ages are ]

• Asha age = (7x + 8) years
• Sushma age = (2x + 8) years

A/q

• The ratio of their ages after 8 years will be 5 : 2

$\implies{\rm }$ (7x + 8) : (2x + 8) = 5 : 2

$\implies{\rm }$ (7x + 8) / (2x + 8) = 5/2

$\implies{\rm }$ 2(7x + 8) = 5(2x + 8)

$\implies{\rm }$ 14x + 16 = 10x + 40

$\implies{\rm }$ 14x – 10x = 40 – 16

$\implies{\rm }$ 4x = 24

$\implies{\rm }$ x = 24/4

$\implies{\rm }$ x = 6

So, Their present ages are

➬ Asha'a age = 7(6) = 42 years

➬ Sushma's age = 2(6) = 12 years