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

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

### 2 thoughts on “Raj’s age is thrice the age of Aryan. Find Aryan’s age if sum of their ages is 64.​”

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 .

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❍ 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,

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

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

• Rajs age is thrice the age of Aryan.

• Raj’s age + Aryan’s age = 64

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

• Aryan’s age = ?

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

Let us assume :

• Aryan’s age to be x

So according to the question

• Raj’s age = 3 × x = 3x

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

According to the question :

Raj’s age + Aryan’s age = 64

• Let’s substitute the values we have assumed

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

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

• 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 :

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

• 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

• Let’s substitute the value that we got

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

$$\sf\dashrightarrow\:64=64$$

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

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

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!! Hope it helps !!