In a village consisting of $p$ persons, $x$% can read and write. Of the males, only $y$% can read and write. Of the females, only $z$% can read and write. If $x, y > z$, then what is the number of males in the village?

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CDS - 2025

In a village consisting of $p$ persons, $x$% can read and write. Of the males, only $y$% can read and write. Of the females, only $z$% can read and write. If $x, y > z$, then what is the number of males in the village?

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CDS 2 2025 Maths Question Paper (14-Sep-2025)

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$p(x-z)/(y-z)$

$p(y-z)/(x-z)$

$px/y$

$py/x$

The correct answer is

$p(x-z)/(y-z)$

Problem Understanding: Finding Village Male Population

The question asks us to determine the total number of males in a village based on its total population, the overall literacy percentage, the literacy percentage among males, and the literacy percentage among females. We are given specific conditions ($x, y > z$) which help ensure the result is meaningful.

Defining Variables for Calculation

Let's define the variables involved in the problem:

Total village population = $p$ persons
Percentage of people who can read and write (literate) = $x$%$
Percentage of males who can read and write (literate males) = $y$%$
Percentage of females who can read and write (literate females) = $z$%$
Let $M$ represent the total number of males in the village.
Let $F$ represent the total number of females in the village.

Setting Up Equations for Literacy

We can express the number of literate individuals using the given percentages:

Total number of literate people in the village = $(x/100) \times p$
Number of literate males = $(y/100) \times M$
Number of literate females = $(z/100) \times F$

The total number of literate people is the sum of literate males and literate females:

$\frac{x}{100} \times p = \left(\frac{y}{100} \times M\right) + \left(\frac{z}{100} \times F\right)$

To simplify, we can multiply the entire equation by 100:

$xp = yM + zF \quad (*)$

Relating Males and Females

We know that the total population is the sum of males and females:

$M + F = p$

From this, we can express the number of females in terms of the number of males and the total population:

$F = p - M$

Solving for the Number of Males

Now, substitute the expression for $F$ into the equation $(*)$:

$xp = yM + z(p - M)$

Distribute $z$ on the right side:

$xp = yM + zp - zM$

Our goal is to find $M$. Let's gather all terms containing $M$ on one side and the other terms on the other side:

$xp - zp = yM - zM$

Factor out $p$ on the left side and $M$ on the right side:

$p(x - z) = M(y - z)$

Finally, isolate $M$ by dividing both sides by $(y - z)$. Note that since we are given $y > z$, the term $(y-z)$ is not zero and is positive.

$M = \frac{p(x - z)}{y - z}$

Conclusion

The derived formula for the number of males in the village is $M = \frac{p(x-z)}{y-z}$. This matches the first option provided.

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