ICSE Class 8 Maths Commercial Arithmetic Chapter 11 Percentage and its Applications

Unit Three: Commercial Arithmetic

Topics Covered:

Percentage and its Applications

Ratio and Proportion

Speed, Distance and Time

Time and Work

Let's Recap

1. Divide the following in the given ratios.

(i) Rs 1584 in a 5 : 7 ratio

(ii) 3 kg 696 g in a 9 : 12 ratio

(iii) 7 l 896 ml in a 11 : 13 ratio

(iv) 42 km 107 m in a 20 : 21 ratio

(v) 1 h 54 min 8 s in a 15 : 17 ratio

2. Find the value of x if the following ratios are in direct proportion.

(i) 27 : 189 and 31 : x

(ii) 41 : 20.5 and x : 32

(iii) 2.55 : x and 3.6 : 5.04

(iv) \(\frac{5}{18} : \frac{1}{6}\) and \(1\frac{1}{4} : x\)

3. 5 gardeners can weed a garden in 3 days. How long will 3 gardeners take to weed the same garden?

4. A man buys a 14" TV for Rs 4176 from an electronics shop advertising a 20% discount. If the marked price of the TV was 45% above its cost price, how much had the shop bought the TV for?

Great news! A big company has agreed to sponsor our club's website. That means our club earns 50 p every time someone visits the site. Imagine, if even 0.1% of all web surfers visit our site, how much money would it lead to? This is when we talk about millions of web surfers!

Don't count your chickens before they are hatched! We'll have to do a bit of arithmetic before we actually start, like placing text and pictures proportionately in a page, deciding as to what percentage of the page should have the sponsor's advertisement, etc. This would involve a lot of work and we've very little time

Percentage And Its Applications

Topics Covered:

Percentage of a Given Measure

Simple Interest

Profit and Loss

Compound Interest

Discount

Introduction

A fraction is a part of a whole, a decimal is a part of a power of 10, and a per cent is a part of 100.

1. To convert a fraction into percentage, multiply the given fraction by 100 and write the symbol '%' after the product.

2. To convert a decimal into percentage, shift the decimal point by two places to the right and write the symbol '%' after the result.

Expressing numbers in percentages is a very common method used in the comparison of measures. By now it must have become a common word in your vocabulary, as you must be using it to compare the marks scored in all the tests you appear for.

Percentage of a Given Measure

Example 1: What is 41% of 7 kg?

41% of 7 kg = \(\frac{41}{100} \times 7 kg = \frac{287}{100}\) kg = 2.87 kg or 2 kg 870 g

Example 2: 24% of a block of ice weighing 4 kg 350 g melted away. What is the weight of ice now?

Method I

24% of 4.35 kg = \(\frac{24}{100} \times 4.35 = \frac{104.4}{100}\) = 1.044 kg

Remaining ice = 4.35 - 1.044 = 3.306 kg = 3 kg 306 g

Method II

Melted percentage of ice = 24%

Remaining percentage of ice = 100 - 24 = 76%

Hence, 76% of 4.35 kg = 3.306 kg or 3 kg 306 g

Measure as a Percentage of Another Measure

Example 3: 7l 524 ml of an 8l 550 ml solution is water. Express it in percentage.

Measure as percentage of another measure = \(\frac{\text{First measure}}{\text{Second measure}} \times 100\%\) = \(\frac{7.524}{8.550} \times 100\%\) = 88%

Thus, 7l 524 ml of water is 88% of the 8 l 550 ml solution.

Example 4: Out of 8400 candidates who sat for an entrance examination, only 294 passed. What was the percentage of failures in that examination?

Number of failures = 8400 - 294 = 8106

Percentage of failures = \(\frac{8106}{8400} \times 100\%\) = 96.5%

Try this!

1. Express 56% as a fraction.

2. Express 0.2% as a decimal.

Word Problems

Example 5: Prachi's father gives her 5% of his monthly salary to spend on her birthday. She saves 60% of the money given to her and spends 25% of the rest on a doll. If the doll costs Rs 139.50, how much does Prachee's father earn?

She saves 60%. She spends remaining 40%. Out of 40%, she spends 25% on a doll.

25% of money spent = Rs 139.50

\(\Rightarrow \frac{25}{100}\) of money spent = Rs 139.50

\(\Rightarrow\) Money spent = \(\frac{139.50 \times 100}{25}\) = Rs 558

Now money spent = (100% - 60%) of money received = Rs 558

or Rs 558 = 40% of money received from her father

or \(\frac{40}{100}\) of money received = Rs 558

\(\Rightarrow\) Money received = \(\frac{558 \times 100}{40}\) = Rs 1395.00

Now money received = 5% of father's salary

or Rs 1395 = \(\frac{5}{100}\) of father's salary

\(\Rightarrow\) Father's salary = \(\frac{1395 \times 100}{5}\) = Rs 27900.00

Example 6: 50% of the people in a restaurant are tea drinkers, 35% are coffee drinkers while 20% drink coffee as well as tea. If 8 people drink coffee as well as tea, how many people in the restaurant drink neither coffee nor tea?

Let us use a Venn diagram to help us solve this problem.

Percentage of people who drink tea, but not coffee = 50% - 20% = 30%

Percentage of people who drink coffee, but not tea = 35% - 20% = 15%

Thus, people who drink either tea or coffee = 30% + 20% + 15% = 65%

Thus, people who drink neither tea nor coffee = 100% - 65% = 35%

Number of people who drink both coffee and tea = 8

Given 20% of total people = 8

or \(\frac{20}{100}\) of total people = 8

\(\Rightarrow\) Total people in the restaurant = \(\frac{8 \times 100}{20}\) = 40

Number of people who drink neither tea nor coffee = 35% of 40 people = \(\frac{35}{100} \times 40\) people = 14 people

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