Question

the age of sonal and manoj are in ratio7:5, ten year hence the ratio of their age will be 9:7 find there present age​

Answer 1

Answer:

$\huge \pink{ \underline{ \boxed{ \mathbb{AnSwEr: - }}}}$

Step-by-step explanation:

$Let \: the \: age \: of \: sonal \: be = 7x \\ Let \: the \: age \: of \: manoj \: be = 5x \\ After \: Ten \: years \: their \: age \: will \: be =9:7 \\ After \: Ten \: years = \frac{7x+10}{5x+10}=\frac{9}{7} \\ \frac{7x + 10}{5x + 10} = \frac{9}{7} \\ \frac{7x + 10}{5x + 10} \times \frac{9}{7} \\ 7(7x + 10) = 9(5x + 10) \\ 49x + 70 = 45x + 90 \\ 49x - 45x = 90 - 70 \\ 4x = 20 \\ x = \frac{20}{4} \\ x = 5 \\ Age \: of \: Sonal = 7x = 7(5) = 35 \: years \\ Age \: of \: Manoj = 5x = 5(5) = 25 \: years.$

HOPE IT WILL HELP YOU.....

Answer 2

Given :

• Age of Sonal and Manoj are in the ratio 7:5 .
• After Ten years the ratio of their ages will be 9:7 .

To Find :

• Present Age of Sonal and Manoj .

Solution :

$\longmapsto\tt{Let\:Present\:Age\:of\:Sonal\:be=7x}$

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

After 10 years :

$\longmapsto\tt{Age\:of\:Sonal=7x+10}$

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

A.T.Q :

$\longmapsto\tt{\dfrac{7x+10}{5x+10}=\dfrac{9}{7}}$

$\longmapsto\tt{7(7x+10)=9(5x+10)}$

$\longmapsto\tt{49x+70=45x+90}$

$\longmapsto\tt{49x-45x=90-70}$

$\longmapsto\tt{4x=20}$

$\longmapsto\tt{x=\cancel\dfrac{20}{4}}$

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

Value of x is 20 ...

Therefore :

$\longmapsto\tt{Present\:Age\:of\:Sonal=7(5)}$

$\longmapsto\tt\bf{35\:yrs.}$

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

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