Question

Four years ago, the ratio of age of Akash and Beena was 3:4. Seventeen year hence the ratio of their age will be 6:7. what is the present age of akash?​

Answer 1

Step-by-step explanation:

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

• Four years ago, the ratio of age of Akash and Beena was 3:4.

• Seventeen year hence the ratio of their age will be 6:7.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The present age of Akash.

$\bf{\underline{\underline\green{Solution:-}}}$

Let the present age of Akash be x

The present age of Beena be y

$\bf\underline{\pink{Case 1:-}}$

Four years ago:-

Age of Akash = x - 4

Age of Beena = y - 4

Given,Four years ago, the ratio of age of Akash and Beena was 3:4.

So:-

$\rm \implies x - 4 : y - 4 = 3 : 4$

$\rm \implies \dfrac{x - 4}{y - 4} = \dfrac{3}{4}$

By cross multiplication:-

$\rm \implies {4(x - 4)} = {3(y - 4)}$

$\rm \implies {4x - 16} = {3y - 12}$

$\rm \implies {4x - 3y} = { - 12 + 16}$

$\rm \implies {4x - 3y} = { 4.....(i)}$

$\bf\underline{\orange{Case 2:-}}$

Seventeen years hence:-

Age of Akash = x + 17

Age of Beena = y + 17

Given,Seventeen year hence the ratio of their age will be 6:7.

So:-

$\rm \implies x + 17 : y + 17 = 6 : 7$

$\rm \implies \dfrac{x + 17}{y + 17} = \dfrac{6}{7}$

By cross multiplication:-

$\rm \implies {7(x + 17)} = {6(y + 17)}$

$\rm \implies {7x +119} = {6y + 102}$

$\rm \implies {7x - 6y} = { 102 - 119}$

$\rm\implies {7x - 6y} = { - 17} .....(ii)$

Multiplying equation (i) with 2

$\rm\implies 2(4x - 3y = 4)$

$\rm \implies8x - 6y = 8.....(iii)$

Subtracting equation (ii) from (iii)

$\rm \implies8x - 6y - (7x - 6y)= 8 - ( - 17)$

$\rm \implies8x - 6y - 7x + 6y= 8 + 17$

$\rm \implies x= 25$

Present age of Akash = x = 25

$\underline{ \boxed {\purple{\bf\therefore Present \: age \: of \: Akash= 25 \: years}}}$