The ratio of the present ages of Charvi and Vaishnavi is 4 : 5. Yuvika is 2 years older than Charvi but 5 years younger than Vaishnavi. Find the present age of Vaishnavi.
The problem starts by giving us the ratio of the present ages of two individuals, Charvi and Vaishnavi. The ratio is specified as 4:5.
Let's represent their present ages using variables. A common way to handle ratios is to introduce a common multiplier, let's call it '$x$'.
- Charvi's present age = $4x$ years.
- Vaishnavi's present age = $5x$ years.
This representation ensures that the ratio of their ages ($4x : 5x$) is always 4:5.
Relating Yuvika's Age to Charvi and VaishnaviNext, we are given information about a third person, Yuvika, and her age relative to Charvi and Vaishnavi.
- Yuvika is 2 years older than Charvi. This means Yuvika's age can be expressed as: Present Age of Yuvika = Charvi's Present Age + 2 Present Age of Yuvika = $4x + 2$.
- Yuvika is 5 years younger than Vaishnavi. This means Yuvika's age can also be expressed as: Present Age of Yuvika = Vaishnavi's Present Age - 5 Present Age of Yuvika = $5x - 5$.
We now have two different expressions for Yuvika's present age. Since both expressions represent the same age, we can set them equal to each other:
$$4x + 2 = 5x - 5$$Our goal is to solve this equation for '$x$' to find the value of the common multiplier.
- Isolate the variable '$x$': We can rearrange the equation to get all the '$x$' terms on one side and the constant numbers on the other. Let's move the '$x$' terms to the right side and the constants to the left side.
- Subtract $4x$ from both sides: $2 = 5x - 4x - 5$
- Simplify: $2 = x - 5$
- Solve for '$x$': Now, add 5 to both sides of the equation to find the value of $x$.
- $2 + 5 = x$
- $7 = x$
So, the value of our common multiplier '$x$' is 7.
The question asks for the present age of Vaishnavi. We established that Vaishnavi's present age is $5x$. Now we substitute the value of $x$ we found:
Vaishnavi's Present Age = $5x = 5 \times 7 = 35$ years.
Verification of AgesWe can quickly check if our value of $x=7$ satisfies all the conditions given in the problem.
- Charvi's Age = $4x = 4 \times 7 = 28$ years.
- Vaishnavi's Age = $5x = 5 \times 7 = 35$ years.
- The ratio Charvi:Vaishnavi is $28:35$, which simplifies to $4:5$ (dividing both by 7). This matches the given information.
- Yuvika's Age (calculated from Charvi) = Charvi's Age + 2 = $28 + 2 = 30$ years.
- Yuvika's Age (calculated from Vaishnavi) = Vaishnavi's Age - 5 = $35 - 5 = 30$ years.
Both calculations for Yuvika's age give 30 years, confirming that our calculated ages are correct and consistent with all the details provided in the question.
Therefore, the present age of Vaishnavi is 35 years.
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