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The employer decreases the number of his employees in the ratio 10 ∶ 9 and increases their wages in the ratio 11 ∶ 12, then what is the ratio of his two expenditure ?
1. 55 ∶ 54
2. 50 ∶ 45
3. 61 ∶ 57
4. 77 ∶ 84

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Correct Answer - Option 1 : 55 ∶ 54

Given:

Decrement in number of employees = 10 ∶ 9

Increment in wages = 11 ∶ 12

Formula Used: 

The ratio of total expenditure = \(\frac{Number\space of \space workers\space before \space change\times Wage \space per\space worker \space before \space change}{Number\space of \space workers\space after\space change \times Wage \space per\space worker \space after \space change}\)

Calculation:

Let assume the number of employees before decrement = 10x

The number of employees after decrement = 9x

Wages before increment = 11y

Wages after increment = 12y

Ratio of total expenditure = \(\frac{Number\space of \space workers\space before \space change\times Wage \space per\space worker \space before \space change}{Number\space of \space workers\space after\space change \times Wage \space per\space worker \space after \space change}\)

⇒ Ratio of total expenditure = \(\frac{10x \space \times \space11y}{9x\space \times \space 12y}\)

⇒ Ratio of total expenditure = 55 ∶ 54

∴ The ratio of total expenditure = 55 ∶ 54

The correct option is 1 i.e. 55 ∶ 54

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