# Basic Application of Percentages

By per cent, we mean “out of 100.”

If a student gets 27 marks out of 40, and another gets 35 out of 60, can we say that the second student is smarter because he has 35 marks and the first has only 27? We need to know how many marks they have got if the base was 100, so that the figures are comparable. Our problem is to convert 27/40 = x/100 and 35/60 = y/100 and then we can see who is smarter of the two. When we convert the base into 100, we will see that the first student is smarter than the second.

☺**Time saver:**

In the above problem, we can either multiply the fractions by 100 as follows: 27/40 × 100 and 35/60 × 100, which may take some time. But a simple way to convert into percentage is to divide by the simplest from of the denominator and multiplying the result by 10 or 100 as the case may be. In this case the fractions get reduced to 27/4 and 35/6 which yield 6.75 and 5.83 through simple division. Since we have removed one “0” from the denominator, we multiply by 10 to get the percentage, which is 67.5% and 58.3%.

If we say that the stock market index, Sensex, increased by 238 points and closed at 11,860, then we are interested to know how big is the increase. The figures will have significance only when we can find out their relative value on a common index, 100. We should thus find out 238/11622 = x/100.

Note that the base taken is 11622 and not 11860. Students sometimes make the mistake of taking a wrong base.

*Remember that the base to be taken is always the original quantity.*

In this case, the original quantity was calculated by subtracting: 11860 – 238 = 11622.

*Thus x per cent means x/100, written as x%.*

That is, a decimal fraction which has 100 as its denominator is known as Percentage. The numerator of such a fraction is known as Rate Per Cent.

In the above illustration, finding a fraction like 238/11622 may seem daunting, but must be done within a split second by a manager. People use different mental processes to solve the figures. One process can be as follows: we see that the increase is about 240 on a base of about 11700, which can further be approximated to 250/12000 and a quick mental calculation shows that the figure should be slightly more than 2%. [Note that 2% of 12000 is 240]

A manager must develop a brain that calculates these figures in real time.

**Illustration 1**:

**Illustration 2**: