Ten years hence, the respective ratio between Simmi's age ans Niti's age will be 7 ∶ 9. Two years ago, the respective ratio between Simmi's and Niti's age was 1 ∶ 3. If Abhay is 4 years older then Niti, what is Abhay's present age ? (in years) 

Given:

Ten years hence, the ratio between Simmi's age and Niti's age will be 7 ∶ 9.

Two years ago, the ratio between Simmi's age and Niti's age was 1 ∶ 3.

Abhay is 4 years older than Niti.

Concept Used:

We need to set up equations based on the given ratios and solve for the present ages of Simmi and Niti. Then, we use the given information to find Abhay's age.

Calculation:

Let Simmi's present age be S and Niti's present age be N.

Ten years hence:

⇒ (S + 10) / (N + 10) = 7 / 9

⇒ 9(S + 10) = 7(N + 10)    ...(i)

⇒ 9S + 90 = 7N + 70

⇒ 9S - 7N = -20    ...(ii)

Two years ago:

⇒ (S - 2) / (N - 2) = 1 / 3

⇒ 3(S - 2) = (N - 2)    ...(iii)

⇒ 3S - 6 = N - 2

⇒ 3S - N = 4    ...(iv)

Solving equations (ii) and (iv):

From (iv): N = 3S - 4

Substitute N in (ii):

⇒ 9S - 7(3S - 4) = -20

⇒ 9S - 21S + 28 = -20

⇒ -12S = -48

⇒ S = 4

Using S in (iv):

⇒ N = 3(4) - 4

⇒ N = 12 - 4

⇒ N = 8

Abhay's present age:

⇒ Niti's age + 4

⇒ 8 + 4

⇒ 12

∴ Abhay's present age is 12 years.

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