krit.club logo

Fractions in Disguise - Percentage of Some Quantity

Grade 8CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

A percentage is essentially a 'fraction in disguise' where the denominator is always 100100. The symbol %\% represents 1100\frac{1}{100}.

•

To calculate the percentage of a given quantity, we convert the percentage into a fraction and multiply it by the quantity. The word 'of' indicates multiplication (×\times).

•

If we need to find what percent one quantity xx is of another quantity yy, we use the ratio xy\frac{x}{y} and multiply by 100100.

•

Percentages can be expressed as decimals by dividing the percentage value by 100100 (moving the decimal point two places to the left). For example, 45%=0.4545\% = 0.45.

📐Formulae

Value=Percentage100×Total Quantity\text{Value} = \frac{\text{Percentage}}{100} \times \text{Total Quantity}

Percentage=(PartWhole)×100%\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100\%

Total Quantity=Value×100Percentage\text{Total Quantity} = \frac{\text{Value} \times 100}{\text{Percentage}}

💡Examples

Problem 1:

A fruit seller has 400400 kg of apples. If 15%15\% of the apples are found to be rotten, calculate the weight of the rotten apples.

Solution:

Total weight of apples = 400400 kg. Percentage of rotten apples = 15%15\%. Weight of rotten apples = 15%15\% of 400400 kg =15100×400= \frac{15}{100} \times 400 =15×4=60 kg= 15 \times 4 = 60 \text{ kg}

Explanation:

We convert the percentage 15%15\% to the fraction 15100\frac{15}{100} and multiply it by the total quantity (400400 kg) to find the specific part.

Problem 2:

In an exam, Rahul scored 340340 marks out of 400400. Find his percentage of marks.

Solution:

Marks obtained = 340340. Total marks = 400400. Percentage = (340400)×100%\left( \frac{340}{400} \right) \times 100\% =3404%= \frac{340}{4}\% =85%= 85\%

Explanation:

To find the percentage, we create a fraction of the marks obtained over the total marks and multiply by 100100.

Problem 3:

A man saves ₹12,000₹ 12,000 per month, which is 20%20\% of his total monthly income. Find his total monthly income and his expenditure using vertical subtraction.

Solution:

Let the total income be xx. 20%20\% of x=12000x = 12000 20100×x=12000\frac{20}{100} \times x = 12000 x=12000×10020=12000×5=60000x = \frac{12000 \times 100}{20} = 12000 \times 5 = 60000 Total Income = ₹60,000₹ 60,000. To find expenditure (Income - Savings): 60000−1200048000\begin{array}{r} 60000 \\ - 12000 \\ \hline 48000 \end{array} Expenditure = ₹48,000₹ 48,000.

Explanation:

First, we find the whole quantity when a percentage of it is known. Then, we subtract the savings from the total income to find the expenditure.