Calculating Savings from Earnings: A Percentage Problem

This problem asks us to determine how much Pankaj saves from his total earnings after spending a certain percentage. We are given Pankaj's total earning and the percentage he spends. To find the amount he saves, we can either calculate the amount spent and subtract it from the total earning, or calculate the percentage saved and find that percentage of the total earning.

Given Information:

• Total Earning = Rs. 720
• Percentage Spent = 65%

Method 1: Calculate Amount Spent, then Amount Saved

First, let's calculate the amount Pankaj spends. The amount spent is 65% of his total earning, Rs. 720.

Amount Spent $= 65\% \text{ of } 720$

To calculate a percentage of a number, we convert the percentage to a decimal or a fraction and multiply it by the number.

Amount Spent $= \frac{65}{100} \times 720$

Now, let's perform the calculation:

Amount Spent $= \frac{65 \times 720}{100}$

Amount Spent $= \frac{65 \times 72}{10}$

Amount Spent $= 65 \times 7.2$

Amount Spent $= 468$

So, Pankaj spends Rs. 468.

Next, we calculate the amount saved by subtracting the amount spent from the total earning:

Amount Saved = Total Earning - Amount Spent

Amount Saved $= 720 - 468$

Amount Saved $= 252$

Using this method, Pankaj saves Rs. 252.

Method 2: Calculate Percentage Saved, then Amount Saved

Alternatively, if Pankaj spends 65% of his earning, the remaining percentage is what he saves. The total earning represents 100%.

Percentage Saved = 100% - Percentage Spent

Percentage Saved $= 100\% - 65\%$

Percentage Saved $= 35\%$

So, Pankaj saves 35% of his total earning.

Now, we calculate the amount saved, which is 35% of Rs. 720.

Amount Saved $= 35\% \text{ of } 720$

Amount Saved $= \frac{35}{100} \times 720$

Amount Saved $= \frac{35 \times 720}{100}$

Amount Saved $= \frac{35 \times 72}{10}$

Amount Saved $= 35 \times 7.2$

Amount Saved $= 252$

Using this method, Pankaj also saves Rs. 252.

Both methods give us the same result. Pankaj saves Rs. 252.

Comparing with Options

Let's look at the given options:

• Rs. 250
• Rs. 252
• Rs. 253
• Rs. 251

Our calculated amount saved is Rs. 252, which matches one of the options.

Therefore, Pankaj saves Rs. 252.

Revision Table: Percentage and Savings Calculation

Additional Information on Earning, Spending, and Saving

Understanding the relationship between earning, spending, and saving is fundamental in personal finance and basic arithmetic problems.

• Earning: This is the total money received, often referred to as income. In this problem, the total earning is Rs. 720.
• Spending: This is the portion of the earning that is used to buy goods or services. It is also called expenditure. In this problem, Pankaj spends 65% of his earning.
• Saving: This is the portion of the earning that is not spent but kept aside for future use. It is the difference between the total earning and the amount spent.

The basic relationship is: Earning = Spending + Saving

From this relationship, we can derive: Saving = Earning - Spending

Percentages are a way to represent a part of a whole in terms of 100. When dealing with percentages of money, 100% usually represents the total amount (in this case, the total earning).

If a part is expressed as a percentage of the whole, the remaining part is 100% minus that percentage. This is why if 65% is spent, then 100% - 65% = 35% is saved.