Expressing Quantities as Percentages

Have you ever heard your teacher say, "You scored 85% on your test," or seen "50% OFF" on your favourite toy? That's a percentage in action!

Percentages help us compare things easily. Instead of saying "I ate 3 out of 12 chocolates," we can simply say, "I ate 25% of the chocolates!" Much easier, right?

Steps:

1. Make sure both quantities have the same unit (like kg, rupee, etc.).

2. Divide the first quantity by the second.

3. Multiply the result by 100.

\[\text{Percentage}=\left(\frac{\text{First Quantity}}{\text{Second Quantity}}\right)\times100\%\]

(i) 20 kg as a percentage of 200 kg = `20/200` × 100% = 10%

(ii) 60 paise as a percent of ₹3 
(Change ₹3 to paise: ₹3 = 300 paise.)

                                                  = `⁣60/300` × 100% = 20%

Steps:

1. Write the percentage as a fraction.

2. Multiply the fraction with the total quantity.

3. Simplify to get the final value.

\[\text{Percentage of a quantity}=\left(\frac{\mathrm{Given}\%}{100}\right)\times\mathrm{Quantity}\]

1.25% of ₹500 = `25/100` × ₹500 = ₹125

2. 30% of 400 = `30/100` × 400 = ₹120

Example 1 – Real-life School Scenario

In a class of 50 students, 40% are girls. Find the number of girls and the number of boys in the class.

Solution:
No. of girls in the class = 40% of 50 =  `40/100` × 50 = 20
No. of boys in the class = 50 - 20 = 30 

Example 2 – Real-life Report Card Calculation

A girl scored 60 out of 75 in English, 60 out of 90 in mathematics and 80 out of 100 in science. Find the marks scored by her as a percentage:
(i) in Mathematics
(ii) in all the three subjects (as a whole)

Solution:
(i) Percentage score in mathematics = 60 out of 90

                                                            = `60 /90` × 100%

                                                            = `200 /3` %

                                                            = 66 `2 /3` %
(ii) Sum of the maximum marks of all the three subjects = 75 + 90 + 100 = 265
and total score in the three subjects = 60 + 60 + 80 = 200

∴ Percentage score as a whole = `200 /265` × 100%

                                                 = 75 `25 / 53` %

1. "Per-cent" = Per 100 (Remember: cent = 100, like century!)

2. Same units first (Convert kg to kg, rupees to paise, etc.)

3. "as %": Divide, then multiply by 100

4. "% of": Convert % to decimal, then multiply