Percentage - Exercise 9(B)

If 16% of a number is 60, find the number.

Answer

Given:

16% of a number is 60

Let the required number be x.

16% of x = 60

$\Rightarrow x \times \dfrac{16}{100} = 60 \\[1em] \Rightarrow x = 60 \times \dfrac{100}{16} \\[1em] \Rightarrow x = 15 \times \dfrac{100}{4} \\[1em] \Rightarrow x = 15 \times 25 \\[1em] \Rightarrow x = 375$

Hence, the number is 375

If $13\dfrac{1}{3}$% of a number is 90, find the number.

Answer

Given:

$13\dfrac{1}{3}$% of a number is 90

Convert mixed fraction to improper:

$13\dfrac{1}{3}$% = $\dfrac{40}{3}$%.

Let the number be x.

$\dfrac{40}{3}$% of x = 90

$\Rightarrow x \times \dfrac{40}{3 \times 100} = 90 \\[1em] \Rightarrow x \times \dfrac{40}{300} = 90 \\[1em] \Rightarrow x = 90 \times \dfrac{300}{40} \\[1em] \Rightarrow x = 90 \times \dfrac{15}{2} \\[1em] \Rightarrow x = 45 \times 15 \\[1em] \Rightarrow x = 675$

Hence, the number is 675.

If 0.6% of a number is 15, find the number.

Answer

Given:

0.6% of a number is 15

Let the number be x.

0.6% of x = 15

$\Rightarrow x \times \dfrac{0.6}{100} = 15 \\[1em] \Rightarrow x = 15 \times \dfrac{100}{0.6} \\[1em] \Rightarrow x = 15 \times \dfrac{1000}{6} \\[1em] \Rightarrow x = \dfrac{5000}{2} \\[1em] \Rightarrow x = 2500$

Hence, the number is 2500.

If $\dfrac{3}{4}$% of a number is 9, find the number.

Answer

Given:

$\dfrac{3}{4}$% of a number is 9

Let the number be x.

$\dfrac{3}{4}$% of x = 9

$\Rightarrow x \times \dfrac{3}{4 \times 100} = 9 \\[1em] \Rightarrow x \times \dfrac{3}{400} = 9 \\[1em] \Rightarrow x = 9 \times \dfrac{400}{3} \\[1em] \Rightarrow x = 3 \times 400 \\[1em] \Rightarrow x = 1200 \\[1em]$

Hence, the number is 1200.

There are 42 boys and 18 girls in a class. What is the percentage of boys in the class?

Answer

Given:

Boys = 42

Girls = 18

Total students = 42 + 18 = 60.

Percentage of boys =

$\left( \dfrac{\text{Number of boys}}{\text{Total students}} \times 100 \right)$%

= $\left( \dfrac{42}{60} \times 100 \right)$%

= $\left( \dfrac{42}{3} \times 5 \right)$%

= $\left( \dfrac{14}{1} \times 5 \right)$%

= 70%

Percentage of boys in the class = 70%

A team won 6 hockey matches and lost 9 matches. What per cent of the matches did the team win?

Answer

Given:

Won matches = 6

Lost matches = 9

Total matches played = 6 + 9 = 15.

Percentage of matches won =

$\left( \dfrac{\text{Number of won matches}}{\text{Total matches played}} \times 100 \right)$%

= $\left( \dfrac{6}{15} \times 100 \right)$%

= $\left( \dfrac{2}{5} \times 100 \right)$%

= $2 \times 20$%

= 40%

Percentage of matches won = 40%

A batsman scored 75 runs which included 3 boundaries and 8 sixes. What per cent of his total score did he make by running between the wickets?

Answer

Given:

Total runs = 75

Boundaries = 3

Sixes = 8

Runs from boundaries = 3 x 4 = 12 runs.

Runs from sixes = 8 x 6 = 48 runs.

Total runs from hits = 12 + 48 = 60 runs.

Runs made by running = 75 - 60 = 15 runs.

Percentage of runs by running =

$\left( \dfrac{\text{Runs made by running}}{\text{Total runs}} \times 100 \right)$%

= $\left( \dfrac{15}{75} \times 100 \right)$%

= $\left( \dfrac{1}{5} \times 100 \right)$%

= 20%

Percentage of runs by running = 20%

12% of a sum of money is ₹ 42. What is 20% of the same sum?

Answer

Given:

12% of a sum of money is ₹ 42

20% of the same sum = ?

First, find the sum:

Let the sum be x.

$\phantom{=} x \times \dfrac{12}{100} = ₹ 42 \\[1em] \Rightarrow x = ₹ 42 \times \dfrac{100}{12} \\[1em] \Rightarrow x = ₹ 7 \times \dfrac{100}{2} \\[1em] \Rightarrow x = ₹ \dfrac{700}{2} \\[1em] \Rightarrow x = ₹ 350$

Now, find 20% of ₹ 350:

20% of ₹ 350 = $\dfrac{20}{100} \times ₹ 350$

$= ₹ \dfrac{1}{5} \times 350 \\[1em] = ₹ 70$

20% of ₹ 350 = ₹ 70

$6\dfrac{1}{4}$% of a weight is 0.25 kg. What is 45% of this weight?

Answer

Given:

$6\dfrac{1}{4}$% of a weight is 0.25 kg

45% of the weight = ?

Convert mixed to improper fraction:

$6\dfrac{1}{4}$% = $\dfrac{25}{4}$%

Let the total weight be x.

$\phantom{=} x \times \dfrac{25}{4 \times 100} = 0.25 \text{ kg} \\[1em] x \times \dfrac{25}{400} = 0.25 \text{ kg} \\[1em] \Rightarrow x = 0.25 \times \dfrac{400}{25} \text{ kg} \\[1em] \Rightarrow x = 0.25 \times 16 \text{ kg} \\[1em] \Rightarrow x = 4 \text{ kg}$

Now, find 45% of 4 kg:

45% of 4 = $\dfrac{45}{100} \times 4$ kg

$= \dfrac{180}{100} \text{ kg} \\[1em] = \dfrac{9}{5} \text{ kg} \\[1em] = 1.8 \text{ kg}$

45% of 4 kg = 1.8 kg

In a class of 60 pupils, 15% remained absent on a rainy day. How many pupils were present in the class on that day?

Answer

Given:

Total pupils in class = 60

Percentage of pupils absent = 15%

Number of absent pupils = 15% of 60 = $\dfrac{15}{100} \times 60$ = 9

Number of present pupils = Total pupils - Absent pupils

Substituting the values in above, we get:

Number of present pupils = 60 - 9 = 51

51 pupils were present in the class on that day.

The monthly income of Mr. Amit Goel is ₹ 30400. He saves 12.5% of his income and the rest he spends. How much does he spend each month?

Answer

Given:

Monthly income = ₹ 30400

Percentage saved = 12.5%

Percentage spent = (100 - 12.5)% = 87.5%

Amount spent = 87.5% of ₹ 30400

= ₹ $\dfrac{87.5}{100} \times 30400$

= ₹ 87.5 x 304

= ₹ 26600

He spends ₹ 26600 each month.

An ore contains 15% iron. How much ore will be required to get 18 kg of iron?

Answer

Given:

Percentage of iron in ore = 15%

Required quantity of iron = 18 kg

Let the total weight of the ore be x kg.

Then,

15% of x = 18 kg

$\Rightarrow x \times \dfrac{15}{100} = 18 \text{ kg} \\[1em] \Rightarrow x = 18 \times \dfrac{100}{15} \text{ kg} \\[1em] \Rightarrow x = 6 \times \dfrac{100}{5} \text{ kg} \\[1em] \Rightarrow x = 6 \times \dfrac{20}{1} \text{ kg} \\[1em] \Rightarrow x = 6 \times 20 \text{ kg} \\[1em] \Rightarrow x = 120 \text{ kg}$

120 kg of ore will be required to get 18 kg of iron.

A property dealer charges a commission of 2% on the first ₹ 25000 and 1.5% on the remainder. What commission does he charge for selling a plot of land for ₹ 130000?

Answer

Given:

Selling price of plot = ₹ 130000

Commission on first ₹ 25000 = 2%

Commission on remainder = 1.5%

Commission on first part = 2% of ₹ 25000

= ₹ $\dfrac{2}{100} \times 25000$

= ₹ 500

Remainder amount = ₹ 130000 - ₹ 25000 = ₹ 105000

Commission on remainder = 1.5% of ₹ 105000

= ₹ $\dfrac{1.5}{100} \times 105000$

= ₹ 1575

Total Commission = ₹ 500 + ₹ 1575 = ₹ 2075

Charge for selling a plot of land for ₹ 130000 is ₹ 2075.

In an examination, the maximum marks are 850. Rohit gets 34% marks and fails by 17 marks. Find

(i) the passing marks and

(ii) the minimum percentage for passing the examination.

Answer

Given:

Maximum marks = 850

Rohit's percentage = 34%

Failing margin = 17 marks

Rohit's marks = 34% of 850

= $\dfrac{34}{100} \times 850$

= 289

(i) Passing marks = Rohit's marks + Failing margin

Substituting the values in above, we get:

Passing marks = 289 + 17 = 306

Passing marks = 306

(ii) Minimum passing percentage =

$\left( \dfrac{\text{Passing marks}}{\text{Maximum marks}} \times 100 \right)$%

$= \dfrac{306}{850} \times 100 \\[1em] = \dfrac{3060}{85} \\[1em]$

= 36%

The minimum percentage for passing the examination = 36%

A student secures 90%, 60% and 54% marks in three test papers with maximum marks 100, 150 and 200 respectively. Find his aggregate percentage.

Answer

Given:

Test 1: Max 100, Scored 90%

Test 2: Max 150, Scored 60%

Test 3: Max 200, Scored 54%

Marks in Test 1 = 90% of 100

= $\dfrac{90}{100} \times 100$

= 90

Marks in Test 2 = 60% of 150

$= \dfrac{60}{100} \times 150 \\[1em] = \dfrac{60}{2} \times 3 \\[1em] = \dfrac{180}{2} \\[1em] = 90$

Marks in Test 3 = 54% of 200

$\phantom{=} \dfrac{54}{100} \times 200 \\[1em] = \dfrac{54}{1} \times 2 \\[1em] = 108$

Total marks scored = Marks in Test 1 + Marks in Test 2 + Marks in Test 3

Total marks scored = 90 + 90 + 108 = 288

Total maximum marks = 100 + 150 + 200 = 450

Aggregate percentage =

$\dfrac{\text{Total marks scored}}{\text{Total maximum marks}} \times 100$%

= $\left( \dfrac{288}{450} \times 100 \right)$%

= $\dfrac{2880}{45}$%

= 64%

Aggregate percentage = 64%

In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 candidates belonged to other categories, then how many candidates applied for the examination?

Answer

Given:

Ineligible applicants = 5%

General category (of eligible) = 85%

Other categories (of eligible) = 100% - 85% = 15%

Number of "Other category" candidates = 4275

Let the total applicants be x

Eligible candidates = 95% of x

= $\dfrac{95}{100} \times x$

= 0.95x

15% of these eligible candidates = 4275

$\phantom{=} \dfrac{15}{100} \times 0.95x = 4275 \\[1em] 0.15 \times 0.95x = 4275 \\[1em] 0.1425x = 4275 \\[1em] \Rightarrow x = \frac{4275}{0.1425} \\[1em] \Rightarrow x = 30000$

30000 candidates applied for the examination.

Gun-powder contains 75% nitre, 10% sulphur and the rest of it is charcoal. Find the quantity of charcoal in 8 kg of gun-powder.

Answer

Given:

Nitre = 75%

Sulphur = 10%

Charcoal = Rest of the powder

Total quantity = 8 kg

Percentage of charcoal = 100% - (75% + 10%) = 15%

Quantity of charcoal = 15% of 8 kg

$= \dfrac{15}{100} \times 8 \text{ kg} \\[1em] = \dfrac{15}{25} \times 2 \text{ kg} \\[1em] = \dfrac{3}{5} \times 2 \text{ kg} \\[1em] = \dfrac{6}{5} \text{ kg} \\[1em] = 1.2 \text{ kg}$

8 kg of gun-powder contains 1.2 kg of charcoal.

An alloy consists of 13 parts of copper, 7 parts of zinc and 5 parts of nickel. Find the percentage of copper in the alloy.

Answer

Given:

Copper = 13 parts

Zinc = 7 parts

Nickel = 5 parts

Total parts = 13 + 7 + 5 = 25 parts.

Percentage of copper =

$\left( \dfrac{\text{Parts of copper}}{\text{Total parts}} \times 100 \right)$%

= $\dfrac{13}{25} \times 100$%

= $\dfrac{13}{1} \times 4$%

= $13 \times 4$%

= 52%

Percentage of copper in the alloy = 52%.

Two candidates A and B contested an election. The total votes polled were 9650. If A got 54% of the votes, find the number of votes received by each.

Answer

Given:

Total votes = 9650

Candidate A's share = 54%

Votes for A = 54% of 9650

$= \dfrac{54}{100} \times 9650 \\[1em] = \dfrac{27}{50} \times 9650 \\[1em] = \dfrac{27}{1} \times 193 \\[1em] = 5211 \text{ votes}$

Votes for B = Total votes - A's share

Votes for B = 9650 - 5211 = 4439 votes

Votes for A = 5211, Votes for B = 4439

At an election between two candidates, 68 votes were declared invalid. The winning candidate secures 52% of the valid votes and wins by 354 votes. Find the total number of votes polled.

Answer

Given:

Invalid votes = 68

Winner's share of valid votes = 52%

Winner's margin = 354 votes

Let valid votes be x.

Loser's share = 100% - 52% = 48%

Difference (Margin) = 52% - 48% = 4%

4% of x = 354

$= \dfrac{4}{100} \times x = 354 \\[1em] \Rightarrow x = \dfrac{354 \times 100}{4} \\[1em] \Rightarrow x = \dfrac{354 \times 25}{1} \\[1em] \Rightarrow x = 354 \times 25 \\[1em] \Rightarrow x = 8850 \text{ (valid votes)}$

Total votes polled = Valid + Invalid

= 8850 + 68 = 8918 votes.

Total number of votes polled = 8918

The salary of Mrs Sarita is ₹ 32000 per month. 10% of it is deducted by the employer as provident fund. Of the remaining money, she spends 20% on house rent, 46% on food, 14% on the education of children and 10% on other expenses. Rest she saves. Find :

(i) how much is credited each month to her Provident Fund Account.

(ii) how much is spent on food.

(iii) how much is paid as house rent.

(iv) how much is spent on the education of children.

(v) how much does she save every month.

Answer

Given:

Total Salary = ₹ 32000

Provident Fund Deduction = 10% of total Salary

Remaining Money = Total Salary - Provident Fund Deduction

House Rent = 20% of Remaining Money

Food = 46% of Remaining Money

Education = 14% of Remaining Money

Other Expenses = 10% of Remaining Money

(i) Monthly Credit to Provident Fund Account

Provident Fund = 10% of ₹ 32000

$= \dfrac{10}{100} \times ₹ 32000 \\[1em] = ₹ \dfrac{10}{1} \times 320 \\[1em] = ₹ 3200$

₹ 3200 is credited each month to her Provident Fund Account.

(ii) Amount spent on food:

Food = 46% of Remaining Money

Let us calculate Remaining Money:

Remaining Money = Total Salary - Provident Fund Deduction

Remaining Money = ₹ 32000 - ₹ 3200 = ₹ 28800

Food = 46% of Remaining Money

Food = 46% of ₹ 28800

$= ₹ \dfrac{46}{100} \times 28800 \\[1em] = ₹ \dfrac{46}{1} \times 288 \\[1em] = ₹ 46 \times 288 \\[1em] = ₹ 13248$

Amount spent on food = ₹ 13248.

(iii) Amount paid as House Rent

House Rent = 20% of Remaining Money

House Rent = 20% of ₹ 28800

$= ₹ \dfrac{20}{100} \times 28800 \\[1em] = ₹ \dfrac{20}{1} \times 288 \\[1em] = ₹ 20 \times 288 \\[1em] = ₹ 5760$

Amount paid as House Rent = ₹ 5760.

(iv) Amount spent on Education of children:

Education = 14% of Remaining Money

Education = 14% of ₹ 28800

$= ₹ \dfrac{14}{100} \times 28800 \\[1em] = ₹ \dfrac{14}{1} \times 288 \\[1em] = ₹ 14 \times 288 \\[1em] = ₹ 4032$

Amount spent on Education of children = ₹ 4032.

(v) Monthly Savings:

First, let's find the total percentage spent from the remaining money:

Total Spent % = 20% + 46% + 14% + 10% = 90%

Savings % = 100% - 90% = 10%

Savings = 10% of 28800

$= ₹ \dfrac{10}{100} \times 28800 \\[1em] = ₹ \dfrac{10}{1} \times 288 \\[1em] = ₹ 10 \times 288 \\[1em] = ₹ 2880$

Monthly Savings = ₹ 2880.