Question

age of sujith and sunitha are in the ratio 3:4 four years before the age were 5:7find present ages​

Answer 1

Answer :

the present age of Sujith = 24 years

the present age of Sunitha = 32 years

Step-by-step explanation :

⮞ The ages of Sujith and Sunitha are in the ratio 3 : 4

Let

the present age of Sujith = 3x years

the present age of Sunitha = 4x years

⮞ Four years ago, their ages were in the ratio 5 : 7

Four years ago,

  Sujith's age = (3x - 4) years

  Sunitha's age = (4x - 4) years

          $\sf \frac{3x-4}{4x-4} =\frac{5}{7} \\\\ 7(3x-4)=5(4x-4) \\\\ 21x-28=20x-20 \\\\ 21x-20x=28-20 \\\\ x=8$

⇨ 3x = 3(8) = 24

⇨ 4x = 4(8) = 32

Therefore,

the present age of Sujith = 24 years

the present age of Sunitha = 32 years

Verification :

Four years ago,

Sujith's age = 24 - 4 = 20 years

Sunitha's age = 32 - 4 = 28 years

Their ages were in the ratio 5 : 7

     $\sf \frac{20}{28} =\frac{5}{7} \\\\ \frac{4 \times 5}{4 \times 7} =\frac{5}{7} \\\\ \frac{5}{7} =\frac{5}{7} \\\\ LHS=RHS$

Hence verified!

Answer 2

Answer:

the present age of Sujith = 24 years

the present age of Sunitha = 32 years

Step-by-step explanation :

⮞ The ages of Sujith and Sunitha are in the ratio 3 : 4

Let

the present age of Sujith = 3x years

the present age of Sunitha = 4x years

⮞ Four years ago, their ages were in the ratio 5 : 7

Four years ago,

Sujith's age = (3x - 4) years

Sunitha's age = (4x - 4) years

$\begin{gathered}\sf \frac{3x-4}{4x-4} =\frac{5}{7} \\\\ 7(3x-4)=5(4x-4) \\\\ 21x-28=20x-20 \\\\ 21x-20x=28-20 \\\\ x=8\end{gathered}$

7(3x−4)=5(4x−4)

21x−28=20x−20

21x−20x=28−20

x=8

⇨ 3x = 3(8) = 24

⇨ 4x = 4(8) = 32

Therefore,

the present age of Sujith = 24 years

the present age of Sunitha = 32 years

Verification :

Four years ago,

Sujith's age = 24 - 4 = 20 years

Sunitha's age = 32 - 4 = 28 years

Their ages were in the ratio 5 : 7

$\begin{gathered}\sf \frac{20}{28} =\frac{5}{7} \\\\ \frac{4 \times 5}{4 \times 7} =\frac{5}{7} \\\\ \frac{5}{7} =\frac{5}{7} \\\\ LHS=RHS\end{gathered}$

LHS=RHS

Hence verified!