Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old is Nuri?

To solve the problem of Nuri and Sonu's ages, we can set up a couple of equations based on the information provided. Let's break it down step by step.

Setting Up the Variables

First, let's define the current ages of Nuri and Sonu. We can let:

• N = Nuri's current age
• S = Sonu's current age

Creating the Equations

Now, we can translate the information from the problem into mathematical equations.

Equation from Five Years Ago

According to the first piece of information, five years ago, Nuri was three times as old as Sonu. We can express this as:

N - 5 = 3(S - 5)

Expanding this equation gives us:

N - 5 = 3S - 15

Rearranging it leads to:

N = 3S - 10

Equation from Ten Years Later

Next, we consider the second piece of information: ten years from now, Nuri will be twice as old as Sonu. This can be expressed as:

N + 10 = 2(S + 10)

Expanding this equation results in:

N + 10 = 2S + 20

Rearranging gives us:

N = 2S + 10

Solving the System of Equations

Now we have two equations:

• N = 3S - 10
• N = 2S + 10

Since both expressions equal N, we can set them equal to each other:

3S - 10 = 2S + 10

Isolating S

To find Sonu's age, we can isolate S:

• Subtract 2S from both sides: S - 10 = 10
• Add 10 to both sides: S = 20

Finding Nuri's Age

Now that we know Sonu's current age is 20, we can substitute this value back into one of our earlier equations to find Nuri's age. Using the equation N = 2S + 10:

N = 2(20) + 10

N = 40 + 10

N = 50

Final Answer

Thus, Nuri is currently 50 years old.

Verification

To ensure our solution is correct, we can verify both conditions:

• Five years ago, Nuri was 45 and Sonu was 15. Indeed, 45 is three times 15.
• In ten years, Nuri will be 60 and Sonu will be 30. Here, 60 is twice 30.

Both conditions hold true, confirming that Nuri is indeed 50 years old.