Question

The ratio of the ages of a father and his son is 17:7. Six years ago, the ratio of their ages was
3:1. The father's present age is​

Answer 1

Step-by-step explanation:

Given:

• The ratio of the ages of a father and his son
• Six years ago, the ratio of their ages

To Find:

• Father's present age

Solution:

Let the present age of father and son be 7x years and 17x years respectively.

6 years ago,

Father's age was 17x-6 years

Son's age was 7x-6 years

Now, given is that the ratio of 17x-6:7x-6=3:1

ACQ

$\therefore \leadsto \: \tt \frac{17x - 6}{7x - 6} = \frac{3}{1}$

→3(7x-6)=1(17x-6)

→21x-18=17x-6

21x-17x=18+(-6)

4x=12

x=3

Present age of Father=17x=17×3=51 years

Answer 2

★ At present, father is 51 years old.

Step-by-step explanation

Analysis -

⠀⠀⠀In the question, it has been stated that the ages of a father and his son is in the ratio 17 : 7. Before six years, their ages were in the ratio 3 : 1. We've been asked to find the present age of father.

Solution -

⠀⠀⠀Let's say that the present ages of father and son are 17x and 7x, respectively, since their ages has been given in the form of ratio.

Before six years,

• Father's age = (17x – 6) yrs
• Son's age = (7x – 6) yrs

According to the question,

$\twoheadrightarrow{ \sf{ \quad\dfrac{Father's \: age \: _{(6 \: years \: ago)}}{Son's \: age \: _{(6 \: years \: ago)}} = 3 : 1}}$

$\twoheadrightarrow{ \sf{ \quad \dfrac{(17x - 6)}{(7x - 6)} = 3 : 1 }}$

$\twoheadrightarrow{ \sf{ \quad \dfrac{(17x - 6)}{(7x - 6)} = \dfrac{3}{1} }}$

$\twoheadrightarrow{ \sf{ \quad 1(17x - 6) = 3(7x - 6)}}$

$\twoheadrightarrow{ \sf{ \quad 17x - 6 = 21x - 18}}$

$\twoheadrightarrow{ \sf{ \quad 17x - 21x = - 18 + 6}}$

$\twoheadrightarrow{ \sf{ \quad - 4x = - 18 + 6}}$

$\twoheadrightarrow{ \sf{ \quad - 4x = - 12}}$

$\twoheadrightarrow{ \sf{ \quad x = \dfrac{ \cancel{- 12}}{ \cancel{- 4}} }}$

$\twoheadrightarrow{ \quad \boxed{ \frak{ \pmb{x = 3}}}}$

We've obtained the value of x. So, let's plug in its value in the expression formed for the present age of father.

• Father's present age:

⠀⠀⠀⠀⠀⠀⠀⠀= 17x = 17(3)

⠀⠀⠀⠀⠀⠀⠀⠀= $\underline{\boxed{\frak{\red{\pmb{51}}\: \sf\pmb{years}}}}$

Verification -

Substitute the value of x in the equation formed.

$\twoheadrightarrow{ \sf{ \quad \dfrac{(17x - 6)}{(7x - 6)} = 3 : 1 }}$

$\twoheadrightarrow{ \sf{ \quad \dfrac{17 \times 3 - 6}{7 \times 3 - 6} = \dfrac{3}{1} }}$

$\twoheadrightarrow{ \sf{ \quad \dfrac{51 - 6}{21 - 6} = \dfrac{3}{1} }}$

$\twoheadrightarrow{ \sf{ \quad \dfrac{45}{15} = \dfrac{3}{1} }}$

$\twoheadrightarrow{ \sf{ \quad \dfrac{ \cancel{15}(3)}{ \cancel{15}(1)} = \dfrac{3}{1} }}$

$\twoheadrightarrow{ \sf{ \quad \dfrac{3}{1} = \dfrac{3}{1} }}$

The value of L.H.S. is equal to the value of R.H.S.

Conclusion -

The present age of father is 51 years.

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