Question

Raj's age is thrice the age of Aryan. Find Aryan's age if sum of their ages is 64.​

Answer 1

Given : Raj's age is thrice the age of Aryan & the Sum of their ages is 64 .

Need To Find : The Aryan's age .

⠀⠀⠀⠀ ⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's Consider age of Aryan's be x yrs .

Given that ,

⠀⠀⠀⠀⠀Raj's age is thrice the age of Aryan.

Therefore,

• Raj's age is 3x yrs .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:\:According \:\:\:To\:\:\:Question\: \::}}$

• The sum of their ages is 64 .

$\qquad \longmapsto \sf 3x + x = 64$

$\qquad \longmapsto \sf 4 x = 64$

$\qquad \longmapsto \sf x = \cancel {\dfrac{64}{4}}$

$\qquad \longmapsto \frak{\underline{\purple{\:x = 16 yrs }} }\bigstar$

Therefore,

• Aryan's age is x = 16 yrs .
• Raj's age is 3x = 3(16) = 48 yrs .

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Aryan's \:age \: \:is\:\bf{16 \:yrs.}}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

Answer 2

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

• Rajs age is thrice the age of Aryan.

‎

• Raj's age + Aryan's age = 64

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‎

$\large\sf\underline{To\:find\::}$

• Aryan's age = ?

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‎

$\large\sf\underline{Assumption\::}$

Let us assume :

• Aryan's age to be x

So according to the question

• Raj's age = 3 × x = 3x

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‎

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

According to the question :

Raj's age + Aryan's age = 64

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• Let's substitute the values we have assumed

‎

$\sf\longmapsto\:3x+x=64$

$\sf\longmapsto\:4x=64$

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• Transposing 4 to the other side

‎

$\sf\longmapsto\:x=\cancel{\frac{64}{4}}$

◎ $\small\fbox\red{x\:=\:16}$

‎

‎

Now let's substitute the value of x in the assumed values :

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• Aryan's age = $\small{\mathfrak\orange{16\:yrs}}$ ★

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• Raj's age = 3 × 16 = $\small{\mathfrak\orange{48\:yrs}}$ ★

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_____________________________

$\large\sf\underline{Verifying\::}$

Raj's age + Aryan's age = 64

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• Let's substitute the value that we got

$\sf\dashrightarrow\:48+16=64$

$\sf\dashrightarrow\:64=64$

$\small\fbox\blue{Hence\:Verified}$

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‎

$\dag\:\underline{\sf So\:the\:required\:age\:of\:Aryan\:is\:16\:yrs}$ .

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_____________________________

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!! Hope it helps !!