NIMCET 2012 — Reasoning PYQ

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Question

NIMCET 2012 — Reasoning PYQ

NIMCET | Reasoning | 2012

In a club, there are certain number of males and females. If 15 females are absent, then number of males will be half of females. If 45 males are absent, then female strength will be 5 times that of males. Number of males actually present is

Choose the correct answer:

Explanation

1. Assume Variables

Let the number of males be $M$ and the number of females be $F$ .

2. Formulate Equations based on conditions

Condition 1: If 15 females are absent ( $F - 15$ ), the number of males is half of the remaining females.

$M = \frac{1}{2}(F - 15)$

Multiplying by 2:

$2M = F - 15$

$F = 2M + 15 \quad \dots \text{(Equation 1)}$
Condition 2: If 45 males are absent ( $M - 45$ ), the female strength is 5 times the remaining males.

$F = 5(M - 45) \quad \dots \text{(Equation 2)}$

3. Solve the Equations

Substitute the value of $F$ from Equation 1 into Equation 2:

2M + 15 = 5(M - 45)

2M + 15 = 5M - 225

Rearranging the terms to solve for $M$ :

15 + 225 = 5M - 2M

240 = 3M

M = \frac{240}{3}

M = 80

Conclusion:

The number of males actually present in the club is 80.

Correct Option:

(b) 80