Question

find the age of child whose age is two third of his elder brother, after 5 years he will be four fifth of the elder brothers age. how old is the child​

Answer 1

Answer:

The child is 5 years old.

Step-by-step explanation:

Let us take the ratio as 2 : 3 for the present age.

Then, (2x + 5) / (3x + 5) = 4/5

By cross-multiplication, 5 (2x + 5) = 4 (3x + 5)

                                     = 10x + 25 = 12x + 20

                                     = 25 - 20 = 12x - 10x

                                     = 5 = 2x

                                      = x = 2.5

Thus, the child is 5 years and his brother is 7.5 years old

Answer 2

Answer:

The present age of child is 5 years

Step-by-step explanation:

Let the present age of elder brother be x

We are given that the age of child  is two third of his elder brother.

Present age of child = $\frac{2}{3}x$

Elder brother's age after 5 years = x+5

Child's age after 5 years =  $\frac{2}{3}x+5$

Now we are given that after 5 years he will be four fifth of the elder brothers age.

$\frac{2}{3}x+5=\frac{4}{5}(x+5)$

$\frac{2}{3}x+5=\frac{4}{5}x+4$

$1=\frac{4}{5}x-\frac{2}{3}x$

$1=\frac{2x}{15}$

$\frac{15}{2}=x$

$7.5=x$

Present age of child = $\frac{2}{3}(7.5)=5$

Hence The present age of child is 5 years .