Question

My salary is Rs. 12345 per month. The salary of my brother is \(10 \%\) greater than that of mine. The salary of my only sister is \(9.09 \%\) greater than my only brother. The salary of my wife is\(56 \frac{12}{23} \%\) less than the total salary of my brother and sister together, then the salary of my wife is : (a) greater than my sister's salary (b) \(33 \frac{11}{23} \%\) less than my sister's salary (c) equal to my salary (d) \(44 \frac{11}{22} \%\) greater than my own salary

Short answer

Answer: (b) 33.11/23% less than sister's salary

Step-by-step solution

Calculate the brother's salary

To calculate brother's salary, we can take the person's salary which is Rs.12345 and multiply it by (1+10/100). That is: Brother's salary = 12345 * (1 + 10/100)

Calculate the sister's salary

Sister's salary is 9.09% greater than brother's salary, so we can take brother's salary multiply it by (1+9.09/100). That is: Sister's salary = Brother's salary * (1 + 9.09/100)

Calculate the combined salary of the brother and sister

To do this, we simply add the brother's salary and sister's salary: Combined salary = Brother's salary + Sister's salary

Calculate the wife's salary

Wife's salary is 56.12/23% less than the combined salary of the brother and sister. So we can take combined salary and multiply it by (1 - 56.12/23/100): Wife's salary = Combined salary * (1 - 56.12/23/100)

Compare wife's salary with other salaries

Now we need to compare the wife's salary with the salaries of the person, brother and sister to see which option is correct: (a) greater than sister's salary (b) 33.11/23% less than sister's salary (c) equal to person's salary (d) 44.11/22% greater than person's salary After calculating all the salaries and comparing them, we should be able to find the correct option for the wife's salary in relation to others.

Key concepts

Salary Comparison

Understanding salary comparison is essential when analyzing differences in income. In this exercise, we are looking at multiple salaries: the person's salary, his brother's, his sister's, and his wife's salary. With the given percentage increases and decreases, it can be easily determined how each salary differs from one another, offering insights into their relative financial standings.
We begin with the person's salary, which serves as the base figure of Rs. 12345. By comparison, the brother's salary is 10% higher. To find this, multiply the person's salary by 1.10. Similarly, the sister's salary is 9.09% more than the brother's salary; by multiplying the brother's salary by 1.0909, we obtain the sister's salary.
The wife's salary is reviewed in relation to the combined salary of the brother and sister. Calculating her salary involves understanding that it is 56.12/23% less than this combined figure, requiring careful computation to draw an accurate comparison among all four individuals.

Mathematical Operations

Mathematical operations are at the heart of calculating percentage increases and decreases. Let's break down the process used in this exercise to help you grasp the essential operations.
First, a percentage increase is simply about finding how much extra is being added to the original amount. The operation involves multiplying the original value by

• (1 + percentage increase/100)

This formula is used to determine both the brother's and sister's salaries from their respective increases.
Next, for a percentage decrease, which is needed for calculating the wife's salary, the operation involves multiplying the original combined value of the brother's and sister's salaries by

• (1 - percentage decrease/100)

These operations help in finding the exact salary figures from given percentages and ensure that each calculation is accurate and meaningful.

Problem Solving Steps

Solving a percentage problem methodically aids in reducing errors and gaining clarity. This problem is effectively tackled through a series of steps, which simplifies the overall complexity. Let's go over the steps again as they apply to this exercise.

• Step 1: Begin by calculating the brother's salary. Take the person's salary of Rs. 12345 and multiply by \(1 + \frac{10}{100}\).
• Step 2: With the brother's salary known, determine the sister's salary by multiplying it by \(1 + \frac{9.09}{100}\).
• Step 3: Next, add the brother's and sister's salaries to get a combined total.
• Step 4: Calculate the wife's salary from this combined total by applying the percentage decrease: multiply by \(1 - \frac{56.12}{23}{100}\).
• Step 5: Finally, compare the wife's salary to the other three to determine her standing among the given options: (a) greater than sister's salary, (b) less than sister's salary by a certain percentage, (c) equal to the original salary, or (d) greater by a specific percentage.

This thorough approach not only assists in handling complex calculations but also strengthens problem-solving skills in other percentage-related exercises.