Question

rahman's age is three times the sum of his two sons after 5 years his age will be twice the sum of age of his persons find the age of Rahman's in substitution method​

Answer 1

GIVEN :-

• Rahman's age is three times the sum of the ages of his two sons

• After 5 years , Rahman's age is twice the sum of age of his two sons

TO FIND :-

• Age of Rahman

SOLUTION :-

Let ,

• Rehman's age be ' z '
• Age of his two sons be ' x ' and ' y '

CASE - I :-

Age of Rahman = Two times the sum of the ages of his two sons

$\implies {\underline {\bold {\boxed {\sf {\pink{z =3( x + y)}}}}}} \longrightarrow \: eq(1)$

CASE - II :-

After 5 years their ages would be ,

• Age of Rahman = z + 5
• Age of his two sons = x + 5 , y + 5

We are given that ,

• Age of Rahman is twice the sum of age of his two sons (after 5 years)

$\implies \sf z + 5 = 2(x + 5 + y + 5)$

From eq(1) ,

$\implies \sf \: 3(x + y) + 5 = 2(x + 5 + y + 5) \\ \\ \implies \sf \: 3x + 3y + 5 = 2(x + y + 10) \\ \\ \implies \sf \: 3x + 3y + 5 = 2x + 2y + 20 \\ \\ \implies \sf \: 3x + 3y + 5 - (2x + 2y + 20) = 0 \\ \\ \implies \sf \: 3x + 3y + 5 - 2x - 2y - 20 = 0 \: \\ \\ \implies \sf \: x + y - 15 = 0 \\ \\ \implies \underline {\bold {\boxed{\sf {\pink{x + y = 15}}}}} \longrightarrow \: eq(2)$

Age of Rahman is given by ,

$\implies \sf \: z = 3(x + y) \\ \\ \implies \sf \: z = 3(15) \\ \\ \implies {\underline {\bold {\boxed {\sf {\blue{z = 45}}}}}}$

∴ The Rahman's age is 45 years

Answer 2

Answer :-

Given :-

Rahman's age is three times the sum of his two sons

After 5 years his age will be twice the sum of age of his persons.

To find :-

Age of Rahman

Solution :-

$\normalsize\purple{\boxed{\sf{⟹Let\: age\: of\: Rehman\: be\: "z"}}}$

$\normalsize\pink{\boxed{\sf{⟹Let\: age\: of\: son's\: be\: "x"\: and\: "y"}}}$

Age of Rahman = Two times the sum of the ages of his two sons

After 5 years their ages would be ,

⟹Age of Rahman =$\normalsize\green{\boxed{\sf{ z + 5}}}$

⟹Age of his two sons = $\normalsize\blue{\boxed{\sf{x + 5 \:, y + 5}}}$

So,

$\mathsf{⟹3(x+y)+5=2(x+5+y+5)}$

$\mathsf{⟹3x+3y+5=2x+10+2y+10}$

$\mathsf{⟹3x+3y+5-2x-10-2y-10=0}$

$\mathsf{⟹3x-2x+3y-2y+5-10-10=0}$

$\mathsf{⟹x+y-15=0}$

$\mathsf{⟹x+y=15}$

Now,

Age of Rahman is,

$\mathsf{⟹z=3(x+y)}$

$\mathsf{⟹z=3(15)}$

$\large\orange{\boxed{\sf{Age\: of\: Rahman=45}}}$

Hope it helps..

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