Question

The ages of Rahul and haroon are in the ratio 3:4. Eight years later the sum of their ages will be 44 years. What are their present ages?​

Answer 1

❍ Let's Consider the Present ages of Rahul and Haroon be 3x yrs & 4x yrs , respectively.

⠀⠀⠀⠀⠀☆⠀After 8 years their ages :

• Age of Rahul : 3x + 8 yrs .
• Age of Haroon : 4x + 8 yrs .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:According \: to \: \: the \: \: Question \::}}$

━━━━ Eight years later the sum of their ages will be 44 years.

$\qquad:\implies \sf After\:8\:yrs \:Rahul's \:age \:\:+ \:\:After\:8\:yrs \:Haroon's \:age \:=\: 44 \:$

$\qquad:\implies \sf 3x + 8 \:\:+ \:\:4x + 8 \:=\: 44 \:$

$\qquad:\implies \sf 3x + 4x \:\:+ \:\:8 + 8 \:=\: 44 \:$

$\qquad:\implies \sf 3x + 4x \:\:+ \:\:16 \:=\: 44 \:$

$\qquad:\implies \sf 7x \:\:+ \:\:16 \:=\: 44 \:$

$\qquad:\implies \sf 7x \:\: \:=\: 44 - 16\:$

$\qquad:\implies \sf 7x \:\: \:=\: 28\:$

$\qquad:\implies \sf x \:\: \:=\: \dfrac{28}{7}\:$

$\qquad:\implies \sf x \:\: \:=\: \cancel {\dfrac{28}{7}}\:$

$\qquad \longmapsto \frak{\underline{\purple{\:x \:\:=\:\: 4 \:yrs\:\: }} }\bigstar$

Therefore,

• Present age of Rahul is 3x = 3 × 4 = 12 yrs
• Present age of Haroon is 4x = 4 × 4 = 16 yrs

$\qquad \therefore {\underline {\sf \:Hence\:,\:Present \:age\:of\:Rahul \:\:and\:\:Haroon \:\:are\:\bf 12\:yrs\:\& \: 16\:yrs\:, \sf respectively \:.\:}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

Answer 2

Given:

• The ages of Rahul and haroon are in the ratio 3:4

• Eight years later the sum of their ages will be 44 years.

To Find:

• What are the present ages of Rahul and Haroon

Solution:

❍ Let the present ages of

• Rahul be ${\bf{\pink{3x}}}$
• Haroon be ${\bf{\pink{4x}}}$

${ \underline{ \sf{ \bigstar \: {According \: to \: the \: question : }}}}$

• After 8 years the sum of their ages will be 44

➼ So, let add up 8 to both of their ages and frame an equation summing up the new ages to 44

${ \underline{ \bf{ \bigstar \: Framing \: an \: equation \: we \: get : }}}$

${ : \implies} \sf \: 3x + 8 + 4x + 8 = 44$

~ Now let's group like terms

${ : \implies} \sf 3x + 4x + 8 + 8 = 44$

~ Adding up the like terms we get

${ : \implies} \sf 7x + 16 = 44$

~Transposing the numerical terms using transposition method

${ : \implies} \sf 7x = 44 - 16$

${ : \implies} \sf 7x = 28$

${ : \implies} \sf x = \dfrac{28}{7}$

${ : \implies} \sf { \purple{ \underline{ \boxed{ \pmb{ \frak{x = 4}}}} \bigstar}}$

• Henceforth the value of x is 4 years

~ Now let's find their present ages

${ : \implies} \sf age \: of \: Rahul = 3x = 3(4) = 12$

${ : \implies} \sf age \: of \: Haroon = 4x = 4(4) = 16 \:$

Therefore:

$\longrightarrow \sf \: The \:present \: age \: of \: Rahul \: is \:12 \: years \: \: \: \\ \\ \longrightarrow \sf \: The \:present \: age \: of \:Haroon \: is \:16 \: years$