Question

Radhe father is 7 times as old as Radhe 1 years ago his father was 9 times as old as Radhe find their present ages
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Answer 1

Answer

$\boxed{\boxed{\mathsf{Radhe's\: Age = 4yrs\: \& \:Father's \: Age = 28yrs}}}$

Step-by-step Explanation :

Given

• Radhe's father is 7 times older than her.
• And one year ago his age was 9times older than Radhe.

To find

• Their present ages.

Solution

Let the

$\mathsf{\longrightarrow \: Present \: age \: Radhe be = X}$

• Now it's said that Father is 7 times Radhe's present age. (Therefore)

$\mathsf{\longrightarrow \: Father's \: age \:= 7x}$

Now,

$\mathsf{\longrightarrow \: One\: year \: ago \: Radhe's \: age \: = x - 1}$

$\mathsf{\longrightarrow \: \therefore \: One\: year \: ago \: Father's \: age \: = 7x - 1}$

• Now it's said that one year ago Father is 9 times Radhe's age. (Therefore)

A/Q Forming Equation we have,

$\mathsf{\longrightarrow \: 7x - 1 = 9(x - 1)}$

$\mathsf{\longrightarrow \: 7x - 1 = 9x - 9}$ ---- (1)

(Taking Constant term to LHS and Variable to RHS we have)

$\mathsf{\longrightarrow \: -1 + 9 = 9x - 7x}$

$\mathsf{\longrightarrow \: 8 = 2x}$

$\mathsf{\longrightarrow \: x = 4}$

Therefore We have ,

$\mathsf{\implies \: Value \: of \: \boxed{x = 4}}$

Putting value of X in assumed form of ages we have

$\mathsf{Present \: age \: of \: Radhe \: = x = 4yrs}$

$\mathsf{Present \: age \: of \: Father \: = 7x \rightarrow \: 7(4) = 28yrs }$

$\rule{300}{1}$

Verification

When Radhe's age = 4yrs

Father's age = 7(4) = 28yrs

And One Year Ago

Radhe's age = 4 - 1 = 3yrs

And father age = 28 - 1 = 27 which is 9(Radhe's age = 3)

Answer 2

$\bold{\underline{\underline{\huge{\sf{AnsWer:}}}}}$

Present Age of Radhe = 4 years

Present age of Father = 28 years

$\bold{\underline{\underline{\huge{\sf{StEp\:by\:stEp\:explanation:}}}}}$

GiVeN :

• Radhe's father is 7 times as old as Radhe
• 1 years ago his father was 9 times as old as Radhe.

To FiNd :

• Present age of Father
• Present age of Radhe

SoLuTiOn :

Let the present age of Radhe be x years.

$\sf{\underline{\underline{As\:per\:the\:first\:condition:}}}$

• Radhe's father is 7 times as old as Radhe

$\sf{\therefore{Present\:age\:of\:father\:=\:7x\:years}}$

$\sf{\underline{\underline{As\:per\:the\:second\:condition:}}}$

• 1 years ago his father was 9 times as old as Radhe.

$\sf{\underline{Age\:1\:year\:ago:}}$

$\sf{Father\:=\:7x\:-\:1\:}$

$\sf{Radhe\:=\:x\:-\:1}$

Constituting condition mathematically,

$\hookrightarrow$ $\sf{7x-1\:=\:9\:(x-1)}$

$\hookrightarrow$ $\sf{7x-1\:=\:9x\:-\:9}$

$\hookrightarrow$ $\sf{7x\:-\:9x\:=\:-9\:+\:1}$

$\hookrightarrow$$\sf{-2x\:=\:-\:8}$

$\hookrightarrow$ $\sf{2x\:=\:8}$

$\hookrightarrow$ $\sf{x\:=\:{\dfrac{8}{2}}}$

$\hookrightarrow$ $\sf{x\:=\:4}$

Substitute,x = 4 in assumed age of Father,

$\hookrightarrow$ $\sf{7x}$

$\hookrightarrow$ $\sf{7\:\times\:4}$

$\hookrightarrow$ $\sf{28}$

Present Age :

$\sf{\large{\boxed{\sf{\therefore{Present\:age\:of\:Radhe\:=\:x\:=\:4\:years}}}}}$

$\sf{\large{\boxed{\sf{\therefore{Present\:age\:of\:Radhe's\:Father\:=\:7x\:=\:28\:years}}}}}$