The present age (in years) of Arun is one year less than two times the present age (in years) of Varun. After 5 years from now, Varun's age will be equal to two-third of the present age of Arun. What is the sum of ages (in years) of Arun and Varun, after 2 years from now?

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Delhi Police Head Constable (AWO/TPO) Official Paper (Held On : 27 Oct 2022 Shift 2)

Answer 1

Calculation:

Let Arun's present age be A years.

Let Varun's present age be V years.

According to the first statement: A = 2V - 1 (Equation 1)

After 5 years from now:

Varun's age will be V + 5 years.

According to the second statement: V + 5 = (2/3)A (Equation 2)

The sum of the ages of Arun and Varun after 2 years from now, which is (A + 2) + (V + 2) = A + V + 4.

Substitute the value of A from Equation 1 into Equation 2:

V + 5 = (2/3)(2V - 1)

⇒ 3(V + 5) = 2(2V - 1)

⇒ 3V + 15 = 4V - 2

⇒ 15 + 2 = 4V - 3V

⇒ 17 = V

Varun's present age (V) = 17 years.

Now substitute the value of V back into Equation 1 to find Arun's present age (A):

A = 2(17) - 1

A = 34 - 1

A = 33

Arun's present age (A) = 33 years.

We need to find the sum of their ages after 2 years from now:

Arun's age after 2 years = A + 2 = 33 + 2 = 35 years.

Varun's age after 2 years = V + 2 = 17 + 2 = 19 years.

Sum of their ages after 2 years = 35 + 19 = 54 years.

Alternatively, we can calculate A + V + 4:

A + V + 4 = 33 + 17 + 4 = 50 + 4 = 54 years.

The sum of the ages of Arun and Varun after 2 years from now is 54 years.