Calculating Ratio of Varun's Income

The question asks us to find the ratio of Varun's salary to his income from sources other than salary based on the provided table showing employee income in December 2020.

First, we need to identify Varun's salary and his income from other sources from the table.

• Varun's Salary = Rs. 42000

Varun's income from sources other than salary includes Arrears, Bonus, and Overtime.

• Varun's Arrears = Rs. 7500
• Varun's Bonus = Rs. 1240
• Varun's Overtime = Rs. 1500

Now, we calculate Varun's total income from sources other than salary:

\text{Total other income} = \text{Arrears} + \text{Bonus} + \text{Overtime}

\text{Total other income} = 7500 + 1240 + 1500

\text{Total other income} = 10240

So, Varun's income other than salary is Rs. 10240.

The question asks for the ratio of Varun's salary to his income other than salary.

\text{Ratio} = \frac{\text{Varun's Salary}}{\text{Varun's Total Other Income}}

\text{Ratio} = \frac{42000}{10240}

Now, we need to simplify this ratio.

Start by dividing both numbers by a common factor, like 10:

\frac{42000}{10240} = \frac{4200}{1024}

Divide both by 4:

\frac{4200 \div 4}{1024 \div 4} = \frac{1050}{256}

Divide both by 2:

\frac{1050 \div 2}{256 \div 2} = \frac{525}{128}

The ratio is 525 : 128. Let's check if 525 and 128 have any common factors other than 1.

• Factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175, 525.
• Factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128.

There are no common factors other than 1. So, the ratio 525 : 128 is in its simplest form.

Therefore, the ratio of salary of Varun to his income other than salary is 525 : 128.

Revision Table: Key Data Points

Additional Information: Understanding Ratios

A ratio is a comparison of two quantities. It shows how many times one quantity contains the other. Ratios can be written in several ways:

• Using a colon (:) - e.g., 525 : 128
• As a fraction - e.g., \(\frac{525}{128}\)
• Using the word "to" - e.g., 525 to 128

Ratios are typically simplified to their lowest terms by dividing both parts of the ratio by their greatest common divisor (GCD).

In this problem, we compared Varun's salary to the sum of his other income components (arrears, bonus, overtime) as given in the December 2020 income table.