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A company reduces his employee in the ratio 14 : 12 and increases their wages in the ratio 16:18, Determine whether the bill of wages increases or not and in what ratio.
- a)Decreases, 28: 27
- b)Increases, 27:28
- c)Decreases, 29:28
- d)Increases, 28:29
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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A company reduces his employee in the ratio 14 : 12 and increases thei...
Answer – a) Decreases, 28: 27 Explanation : Let initial employee be 14a and final employee be 12a similarly initial wage is 16b and final wage be 18b Total initial wage = 14a * 16b = 224ab, total final wage = 12a* 18b = 216ab So clearly wages decreases and ratio = 224ab: 216ab = 28:27
Most Upvoted Answer
A company reduces his employee in the ratio 14 : 12 and increases thei...
Given:
- Employee ratio reduced = 14:12
- Wages ratio increased = 16:18
To determine if the bill of wages increases or not and in what ratio, we need to use the concept of direct variation.
Direct Variation: If y is directly proportional to x, then y = kx, where k is the constant of proportionality.
Let the original number of employees be 14x and their original wages be 16y. After the reduction in employees and increase in wages, the new number of employees and their new wages will be 12x and 18y respectively.
We can set up the equation using direct variation as follows:
(14x/12x) = (16y/18y)
Simplifying the equation, we get:
7/6 = 8/9
This equation is not true, which means there is a contradiction. Therefore, the bill of wages does not increase.
To find the ratio in which the bill of wages decreases, we can use the new wages and original wages:
New wages = 18y, Original wages = 16y
The ratio of new wages to original wages is:
18y/16y = 9/8
Therefore, the bill of wages decreases in the ratio 28:27 (9/8 reduced to the lowest terms gives 28/27).
Hence, the correct answer is option A) Decreases, 28:27.
- Employee ratio reduced = 14:12
- Wages ratio increased = 16:18
To determine if the bill of wages increases or not and in what ratio, we need to use the concept of direct variation.
Direct Variation: If y is directly proportional to x, then y = kx, where k is the constant of proportionality.
Let the original number of employees be 14x and their original wages be 16y. After the reduction in employees and increase in wages, the new number of employees and their new wages will be 12x and 18y respectively.
We can set up the equation using direct variation as follows:
(14x/12x) = (16y/18y)
Simplifying the equation, we get:
7/6 = 8/9
This equation is not true, which means there is a contradiction. Therefore, the bill of wages does not increase.
To find the ratio in which the bill of wages decreases, we can use the new wages and original wages:
New wages = 18y, Original wages = 16y
The ratio of new wages to original wages is:
18y/16y = 9/8
Therefore, the bill of wages decreases in the ratio 28:27 (9/8 reduced to the lowest terms gives 28/27).
Hence, the correct answer is option A) Decreases, 28:27.
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A company reduces his employee in the ratio 14 : 12 and increases their wages in the ratio 16:18, Determine whether the bill of wages increases or not and in what ratio.a)Decreases, 28: 27b)Increases, 27:28c)Decreases, 29:28d)Increases, 28:29e)None of theseCorrect answer is option 'A'. Can you explain this answer?
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