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 .

    ⠀⠀⠀⠀ ⠀━━━━━━━━━━━━━━━━━━━⠀

    ❍ 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 .

    ⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\:\:According \:\:\:To\:\:\:Question\: \::}}\\[/tex]

    • The sum of their ages is 64 .

    [tex]\qquad \longmapsto \sf 3x + x = 64 \\ [/tex]

    [tex]\qquad \longmapsto \sf 4 x = 64 \\ [/tex]

    [tex]\qquad \longmapsto \sf x = \cancel {\dfrac{64}{4}} \\ [/tex]

    [tex]\qquad \longmapsto \frak{\underline{\purple{\:x = 16 yrs }} }\bigstar \\[/tex]

    Therefore,

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

    Therefore,

    ⠀⠀⠀⠀⠀[tex]\therefore {\underline{ \mathrm {\:Aryan’s \:age \: \:is\:\bf{16 \:yrs.}}}}\\[/tex]

    ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

  2. [tex]\large\sf\underline{Given\::}[/tex]

    • Rajs age is thrice the age of Aryan.

    • Raj’s age + Aryan’s age = 64

    [tex]\large\sf\underline{To\:find\::}[/tex]

    • Aryan’s age = ?

    [tex]\large\sf\underline{Assumption\::}[/tex]

    Let us assume :

    • Aryan’s age to be x

    So according to the question

    • Raj’s age = 3 × x = 3x

    [tex]\large\sf\underline{Solution\::}[/tex]

    According to the question :

    Raj’s age + Aryan’s age = 64

    • Let’s substitute the values we have assumed

    [tex]\sf\longmapsto\:3x+x=64[/tex]

    [tex]\sf\longmapsto\:4x=64[/tex]

    • Transposing 4 to the other side

    [tex]\sf\longmapsto\:x=\cancel{\frac{64}{4}}[/tex]

    ◎ [tex]\small\fbox\red{x\:=\:16}[/tex]

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

    • Aryan’s age = [tex]\small{\mathfrak\orange{16\:yrs}}[/tex] ★

    • Raj’s age = 3 × 16 = [tex]\small{\mathfrak\orange{48\:yrs}}[/tex] ★

    _____________________________

    [tex]\large\sf\underline{Verifying\::}[/tex]

    Raj’s age + Aryan’s age = 64

    • Let’s substitute the value that we got

    [tex]\sf\dashrightarrow\:48+16=64[/tex]

    [tex]\sf\dashrightarrow\:64=64[/tex]

    [tex]\small\fbox\blue{Hence\:Verified}[/tex]

    [tex]\dag\:\underline{\sf So\:the\:required\:age\:of\:Aryan\:is\:16\:yrs}[/tex] .

    _____________________________

    !! Hope it helps !!

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