Question

In a office, 40% of the employees are men and the rest women, Half of the employees are tall and half short If 10% of the employee are men and, short, and 40 employees are women and tall, the number of tall men employees is

Answer 1

The number of tall men employees = 60

Given :

• In a office, 40% of the employees are men and the rest women, Half of the employees are tall and half short

• 10% of the employee are men and, short, and 40 employees are women and tall

To find :

The number of tall men employees

Solution :

Step 1 of 2 :

Form the equation to calculate number of tall men employees

Let number of total employees in the office = 100x

Since 40% of the employees are men

∴ Number of men employees in the office = 40x

∴ Number of women employees in the office

= 100x - 40x

= 60x

Since half of the employees are tall and half short

∴ Number of tall employees in the office = 50x

∴ Number of short employees in the office = 50x

Since 10% of the employee are men and short

∴ Number of employees are men and short = 10x

∴ Number of employees are men and tall

= 40x - 10x

= 30x

Since 40 employees are women and tall

∴ Number of tall employees = Number of employees are women and tall + Number of employees are men tall

$\displaystyle \sf{ \implies }50x = 40 + 30x$

Step 2 of 2 :

Calculate number of tall men employees

$\displaystyle \sf 50x = 40 + 30x$

$\displaystyle \sf{ \implies }50x - 30x = 40$

$\displaystyle \sf{ \implies }20x = 40$

$\displaystyle \sf{ \implies }x = 2$

∴ Number of employees are men and tall

= 30x

= 30 × 2

= 60

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