Understanding the Salary Changes
This problem involves calculating the ratio of initial salaries of two employees, X and Y, after their salaries undergo a series of percentage changes (increases and decreases).
Calculating Employee X's Final Salary
Let the initial salary of employee X be \(S_X\).
- First, X's salary is increased by 12%. The new salary becomes: \(S_X \times (1 + \frac{12}{100}) = S_X \times (1 + 0.12) = 1.12 \times S_X\)
- Next, this new salary is decreased by 10%. The final salary of X is: \((1.12 \times S_X) \times (1 - \frac{10}{100}) = (1.12 \times S_X) \times (1 - 0.10) = (1.12 \times S_X) \times 0.90\)
- Final Salary of X = \(1.008 \times S_X\)
Calculating Employee Y's Final Salary
Let the initial salary of employee Y be \(S_Y\).
- First, Y's salary is increased by 10%. The new salary becomes: \(S_Y \times (1 + \frac{10}{100}) = S_Y \times (1 + 0.10) = 1.10 \times S_Y\)
- Next, this new salary is decreased by 12%. The final salary of Y is: \((1.10 \times S_Y) \times (1 - \frac{12}{100}) = (1.10 \times S_Y) \times (1 - 0.12) = (1.10 \times S_Y) \times 0.88\)
- Final Salary of Y = \(0.968 \times S_Y\)
Determining the Ratio of Initial Salaries
The problem states that their final salaries are equal. Therefore:
Final Salary of X = Final Salary of Y
\(1.008 \times S_X = 0.968 \times S_Y\)
To find the ratio of the initial salary of X to the initial salary of Y (\(S_X : S_Y\)), we rearrange the equation:
\(\frac{S_X}{S_Y} = \frac{0.968}{1.008}\)
Now, we simplify this fraction. We can remove the decimal points by multiplying the numerator and denominator by 1000:
\(\frac{S_X}{S_Y} = \frac{968}{1008}\)
To simplify further, we find the greatest common divisor or divide by common factors. Both numbers are divisible by 8:
- \(968 \div 8 = 121\)
- \(1008 \div 8 = 126\)
So, the simplified ratio is:
\(\frac{S_X}{S_Y} = \frac{121}{126}\)
Therefore, the ratio of the initial salary of X to the initial salary of Y was 121 : 126.
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Important Questions from Percentage
In an examination, 25% of the candidates failed in Mathematics and 12% failed in English. If 10% of the candidates failed in both the subjects and 292 candidates passed in both the subjects, which one of the following is the number of total candidates appeared in the examination?
What is the value of 9% of 5500 + 2.4% of 1100 - 40% of 1600?
Population of a village is 7960 in which 4660 are female. If in that village 60% are literate in which 70% female are literate, then what is the number of literate male ?
The numbers of students of three classes of a school are in the ratio 4 : 5 : 6. If numbers of students in these classes increase by 25%, 20% and 25% respectively, then ratio of numbers of students will become:
In an examination, Ram obtained 20 % more than Ashok but 10% less than Rajesh. If the marks obtained by Ashok is 1080. Then the Percentage marks obtained by Rajesh if the full marks is 2000 ;
