Question

The present age of a father and son
is in the ratio 8:5. If the difference in
their ages is 12 years, what was the
ratio of their ages 3 years ago?​

Answer 1

Answer:

29:17

Step-by-step explanation:

let the present age of the father be 8x and the present age of the son be 5x.

given, the age difference is 12 years

implies that, 8x-5x is 12 years

implies that, 3x is 12 years

implies that, x is 4 years.

therefore present ages of the father and son are 32(8x4) years and 20(5x4) years respectively.

implies that, they were 29 years and 17 years old respectively 3 years ago.

therefore the required ratio is 29:17

Answer 2

GIVEN:

• The present age of a father and son
• is in the ratio 8:5
• If the difference in
• their ages is 12 years

TO FIND:

• What was the ratio of their ages 3 years ago ?

SOLUTION:

Let the father's age be 'x' years

and,

Son's age be 'y' years

CASE:- ❶

➣ The present age of a father and son

The present age of a father and sonis in the ratio 8:5

According to question:-

$\rm{\dashrightarrow \dfrac{x}{y} = \dfrac{8}{5} }$

Use cross product

$\large\bf{\dashrightarrow 5x = 8y...1) }$

CASE:- ❷ 

➣ If the difference in their ages is 12 years.

According to question:-

$\large\bf{\dashrightarrow x - y = 12...2) }$

$\rm{\dashrightarrow x = 12 + y }$

Put the value of 'x' in equation 1)

$\rm{\dashrightarrow 5(12+y) = 8y}$

$\rm{\dashrightarrow 60 + 5y = 8y }$

$\rm{\dashrightarrow 60 = 8y - 5y }$

$\rm{\dashrightarrow 60 =3y }$

$\rm{\dashrightarrow \cancel\dfrac{60}{3} = y }$

$\large\bf{\dashrightarrow 20 = y }$

❝ The Present age of Son is 20 years ❞

Put the value of 'y' in equation 1)

$\rm{\dashrightarrow 5x = 8 \times 20 }$

$\rm{\dashrightarrow 5x = 160 }$

$\rm{\dashrightarrow x = \cancel\dfrac{160}{5} }$

$\large\bf{\dashrightarrow x = 32 }$

❝ The Present age of Father is 32 years ❞

3 years ago, the ages of Father and son were:-

• Father's age = (32-3) = 29 years
• Son's age = (20-3) = 17 years

$\large{\boxed{\bf{ \star \: Ratio = \dfrac{29}{17} \: \star}}}$

❝ Hence, the ratio of the ages of Father and son 3 years ago was 29/17 ❞

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