Question

The ages of Anil and Sunil are in the ratio 2 : 3 . After 15 years, the ratio of
their ages will be 3: 4. Find their present ages

Answer 1

Answer:

$\bigstar{\bold{Present\:age\:of\:Anil=30\:years}}$

$\bigstar{\bold{Present\:age\:of\:Sunil=45\:years}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Ages of Anil and Sunil are in the ratio 2 : 3
• After 15 years, the ratio of their ages will be 3 : 4

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The present ages of Anil and Sunil

$\Large{\underline{\underline{\bf{Solution:}}}}$

➻ Let the prsesent age of Anil be 2 x

➻ Let the present age of Sunil be 3 x

➻ After 15 years, their ages are given by,

    Age of Anil = 2x + 15

    Age of Sunil = 3x + 15

➻ By given,

   2x + 15 : 3x + 15 = 3 : 4

➻ Cross multipying,

   4 (2x + 15) = 3(3x + 15)

   8x + 60 = 9x + 45

   60 - 45 = 9x - 8x

    x = 15

➻ Hence the value of x is 15

➻ The present age of Anil is given by,

    Present age of Anil = 2 × 15

    Present age of Anil = 30 years

➻ Hence the present age of Anil is 30 years

    $\boxed{\bold{Present\:age\:of\:Anil=30\:years}}$

➻ Now the present age of Sunil is given by,

    Present age of Sunil =  3 × 15

    Present age of Sunil = 45 years

➻ Hence the present age of Sunil is 45 years.

    $\boxed{\bold{Present\:age\:of\:Sunil=45\:years}}$

$\Large{\underline{\underline{\bf{Verification:}}}}$

➻ By given,

    Present age of Anil/Present age of Sunil = 2/3

    30/45 = 2/3

    2/3 = 2/3

➻ After 15 years,

   30 + 15/45 + 15 = 3/4

   45/60 = 3/4

Answer 2

Answer:

$\sf Present\:Age \:\:\xrightarrow{After\:15\:Years} \:\:Future\:Age\\{\sf Anil : Sunil \qquad\qquad\: \: \: \: \: \: \: \: \: \: \: Anil: Sunil} \\{ \: \: \: \: \sf 2 \::\:3 \qquad \qquad \qquad\qquad \: \: \: 3 : 4}$

Let the present age of Anil be 2x and Sunil be 3x respectively.

____________________...

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf \dfrac{Anil+15}{Sunil+15}=\dfrac{3}{4}$

$:\implies\sf \dfrac{2x + 15}{3x + 15} = \dfrac{3}{4}$

$:\implies\sf (2x + 15) \times 4= 3 \times (3x + 15)$

$:\implies\sf 8x + 60 = 9x + 45$

$:\implies\sf 60 - 45= 9x - 8x$

$:\implies\:\underline{\boxed{\textsf{ \textbf{ x = 15 years}}}}$

____________________....

☯ $\underline{\boldsymbol{Present\: Age\:of\: Anil\:\&\:Sunil:}}$

$\bullet\:\:\textsf{Anil = 2x = 2(15) = \textbf{30 years}}$

$\bullet\:\:\textsf{Sunil = 3x = 3(15) = \textbf{45 years}}$