Question

the ages of a and b is in the ratio 3 : 5 after 4 years the sum of their age is 48 find their present age.​

Answer 1

$\huge\bf\green{answer:}$

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

• The ages of ‛ a ’ and ‛ b ’ are in the ratio　3:5
• After 4 years, sum of their ages will be 48

$\bf{{\underline{Here}};}$

• Let the ages of ‛ a ’ and ‛ b ’ be 3x and 5x respectively.
• After 4 years, the sum of their ages will be 48

$\sf\implies{3x+4+5x+4=48}$

$\sf\implies{(3x+5x)+(4+4)=48}$

$\sf\implies{8x+8=48}$

$\sf\implies{8x=48-8}$

$\sf\implies{8x=40}$

$\sf\implies{x={\dfrac{40}{8}}}$

$\sf\implies{x={\green{\underline{\underline{\bf 5}}}}}$

$\bf\therefore{{\underline{Present~ages}}:}$

$\sf{3x=3×5={\green{\underline{\underline{\bf 15}}}}}$

$\sf{5x=5×5={\green{\underline{\underline{\bf 25}}}}}$

$\bf\therefore{{\underline{Required~answer}}:}$

$\sf{Present~age~of~‛ a ’={\green{\underline{\underline{\bf 15~years}}}}}$

$\sf{Present~age~of~‛ b ’={\green{\underline{\underline{\bf 25~years}}}}}$

Answer 2

★ Given:

The ages of a and b are in the ratio 3:5.

After 4 years, the sum of their ages is 48.

★ To Find:

Their present ages.

★ Solution:

Let the ages of a and b be 3x and 5x respectively.

After 4 years:

Age of a = 3x + 4

Age of b = 5x + 4

It is given that the sum of their ages is 48.

→ Forming an equation from the given statements:

3x + 4 + 5x + 4 = 48

→ Adding the like terms:

8x + 8 = 48

→ Moving the constant to the RHS:

8x = 48 - 8

→ Doing the operation:

8x = 40

→ So, value of x:

x = 40/8 = 5

So,

Age of a = 3x = 3 x 5 = 15 years

Age of b = 5x = 5 x 5 = 25 years

★ Final Answers:

Age of a = 15 years

Age of b = 25 years

★ Verification

What to do?

We can check whether our answer is correct by checking whether the LHS is equal to the RHS when we add their ages after 4 years.

LHS

3x + 4 + 5x + 4

Substituting the values of 3x and 5x:

= 15 + 4 + 25 + 4

= 19 + 29

= 48

RHS

48

LHS = RHS

Hence verified!