Question

present ages of a and b are jn ratio 2:3.Four years from now the ratio will be 6:7 find their present ages
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Answer 1

★Given :

• Present ages of a and b are in ratio 2:3.
• Four years from now the ratio will be 6:7.

★To find :

• Their present ages.

★Solution :

Given ratio of present ages is 2:3 .

Then,

• Present age of 'a' = 2x years
• Present age of 'b' = 3x years

Four years from now :

Present age + 4 years

• Age of a = 2x + 4 yrs
• Age of b = 3x + 4 yrs

Given that four years from now the ratio will be 6:7.Therefore,

→(2x + 4)/(3x + 4) = 6/7

→7(2x + 4) = 6(3x + 4)

→14x + 28 = 18x + 24

→28 - 24 = 18x - 14x

→4 = 4x

→x = 4/4

→x = 1

We have :

• Present age of 'a' = 2x years
• Present age of 'b' = 3x years

Therefore,

Present age of 'a' = 2(1) = 2years.

Present age of 'b' = 3(1) = 3 years.

____________________

Answer 2

Given:

present ages of a and b are in ratio 2:3.Four years from now the ratio will be 6:7

To Find:

present ages of a and b

Solution:

Let the Ages of a and b be 2x and 3x years.

According to question,

$\dfrac{2x+4}{3x+4}=\dfrac{6}{7}$

$\Rightarrow 7\left(2x+4\right)=6\left(3x+4\right)$

$\Rightarrow\ 14x+28=18x+24$

$\Rightarrow\ 18x-14x=28-24$

$\Rightarrow\ 4x=4$

$\Rightarrow\ x=\dfrac{4}{4}$

$\Rightarrow\ x=1$

Hence, the age of a= 2x= 2 × 1 = 2 years.

And the age of b= 3x = 3 × 1 = 3 years.