Question

Five years ago Anjali's was twice Sarita age. five years hence, there age will be 4:3, Anjali's present age is---​

Answer 1

Answer :

The present age of Anjali = 15 years

Step-by-step explanation :

Let the present age of Anjali be x years

and the present age of Sarita be y years

Five years ago,

Anjali's age = (x - 5) years

Sarita's age = (y - 5) years

Given,

Five years ago Anjali's age was twice the Sarita's age.

       x - 5 = 2(y - 5)

       x - 5 = 2y - 10

       2y - x = 10 - 5

        2y - x = 5

         x = 2y - 5

After five years,

Anjali's age = (x + 5) years

Sarita's age = (y + 5) years

Given,

Their ages will be in the ratio 4 : 3

      $\sf \frac{x+5}{y+5}=\frac{4}{3}$

  3(x + 5) = 4(y + 5)

  3x + 15 = 4y + 20

   3x - 4y = 20 - 15

    3x - 4y = 5

   3(2y - 5) - 4y = 5

   6y - 15 - 4y = 5

    2y = 15 + 5  

     2y = 20

       y = 20/2

        y = 10

=> x = 2y - 5

    x = 2(10) - 5

    x = 20 - 5

    x = 15

The present age of Anjali is 15 years

The present age of Sarita is 10 years

Verification :

• The present age of Anjali is 15 years

• The present age of Sarita is 10 years

Condition - 1 :

Five years ago Anjali's age was twice the Sarita's age

   (15 - 5) = 2(10 - 5)

       10 = 2(5)

        10 = 10

     LHS = RHS

Condition - 2 :

Five years hence, their ages will be in the ratio 4 : 3

     (15 + 5)/(10 + 5) = 4/3

       20/15 = 4/3

        4/3 = 4/3

      LHS = RHS

Hence verified!

Answer 2

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