Question

Ben is three times as otio : as. Cart now. In two years' time Ben will be twice as old as Cart how old is Carl now.​

Answer 1

Appropriate Question:

Ben is three times as Carl now. In two years time, Ben will be twice as old as Carl. How old is Carl now?

Answer:

$\underline{\boxed{ \pmb{\mathfrak { 2 \; years}}}}$

Step-by-step explanation:

As per the provided information in the given question, we have :

• Present age of Ben = 3 times of Carl's age
• In two years time, Ben will be twice as old as Carl.

We've been asked to calculate the present age of Carl.

Let us assume Carl's age as x and Ben's age as y.

Basically, here we need to frame equations as per the question. By solving the equation, we can easily find his age.

― According to the given question, Ben is three times as Carl now and in two years time, Ben will be twice as old as Carl.

E⠀Q⠀U⠀A⠀T⠀I⠀O⠀N⠀( 1 ) :

$\longrightarrow \sf{\quad {Ben's \; age = 3(Carl's \; age) }}$

$\longrightarrow \sf{\quad {y = 3x }}$

E⠀Q⠀U⠀A⠀T⠀I⠀O⠀N⠀( 2 ) :

Also, in two years time, Ben will be twice as old as Carl.

↠ After two years,

• Ben's age = (y + 2) years
• Carl's age = (x + 2) years

$\longrightarrow \sf{\quad { y + 2 = 2(x + 2)}}$

Now, performing multiplication in RHS.

$\longrightarrow \sf{\quad { y + 2 = 2x + 4}}$

Now, substitute the value of y from the equation ( 1 ).

$\longrightarrow \sf{\quad { 3x + 2 = 2x + 4}}$

Transpose the like terms.

$\longrightarrow \sf{\quad { 3x - 2x= 4 - 2}}$

Performing subtraction in both sides.

$\longrightarrow \sf{\quad { x = 2}}$

As, we have supposed Carl' age as x. So,

$\longrightarrow \quad \underline{\boxed { \textbf{\textsf{ Carl's \; Age = 2 \; years}}}}$

Therefore, age of Carl is 2 years.