Rd Sharma 2017 Solutions for Class 7 Math Chapter 1 Integers are provided here with simple step-by-step explanations. These solutions for Integers are extremely popular among Class 7 students for Math Integers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rd Sharma 2017 Book of Class 7 Math Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rd Sharma 2017 Solutions. All Rd Sharma 2017 Solutions for class Class 7 Math are prepared by experts and are 100% accurate.

#### Page No 11.13:

#### Question 1:

Ashu had 24 pages to write. By the evening, he had completed 25% of his work. How many pages were left?

#### Answer:

Total number of pages Ashu had to write = 24

Number of pages Ashu completed by the evening = 25% of 24 = (25/100) × 24 = 600/100 = 6

Pages left for completion = 24 - 6 = 18 pages

#### Page No 11.13:

#### Question 2:

A box contains 60 eggs. Out of which $16\frac{2}{3}\%$ are rotten ones. How many eggs are rotten?

#### Answer:

Total eggs in the bag = 60

Rotten eggs = $16\frac{2}{3}\%\text{of60}=\frac{50}{3}\%\text{of60=}\frac{50}{3\times 100}\times \text{60}=\frac{1}{6}\times 60=10\text{eggs}$

#### Page No 11.13:

#### Question 3:

Rohit obtained 45 marks out of 80. What per cent marks did he get.

#### Answer:

Marks obtained by Rohit = 45/80

Percentage of marks that Rohit obtained = (45/80) × 100 = $\frac{45}{80}\times 100=\frac{45\times 100}{80}=\frac{450}{8}=\frac{225}{4}=56\frac{1}{4}$

#### Page No 11.13:

#### Question 4:

Mr Virmani saves 12% of his salary. If he receives Rs 15900 per month as salary, find his monthly expenditure.

#### Answer:

Mr. Virmani's salary = Rs. 15900 per month

Mr. Virmani's savings = 12% of Rs. 15900 = (12/100) × 15900 = Rs. 1908

Mr. Virmani's monthly expenditure = Rs. (15900 - 1908) = Rs. 13992

#### Page No 11.13:

#### Question 5:

A lawyer willed his 3 sons Rs 250000 to be divided into portions 30%, 45% and 25%. How much did each of them inherit?

#### Answer:

Total amount with the lawyer = Rs. 250000

First son's inheritance = 30% of 250000 = (30/100) × 250000 = 7500000/100 = Rs. 75000

Second son's inheritance = 45% of 250000 = (45/1000) × 250000 = 11250000/100 = Rs. 112500

Third son's inheritance = 25% of 250000 = (25/100) × 250000 = 6250000/100 = Rs. 62500

#### Page No 11.13:

#### Question 6:

Rajdhani College has 2400 students, 40% of whom are girls. How many boys are there inthe college?

#### Answer:

Total number of students in Rajdhani College = 2400

Number of girls = 40% of 2400 = (40/100) × 2400 = 96000/100 = 960

Number of boys = 2400 - 960 = 1440 boys

#### Page No 11.13:

#### Question 7:

Aman obtained 410 marks out of 500 in CBSE XII examination while his brother Anish gets 536 marks out of 600 in IX class examination. Find whose performance is better?

#### Answer:

Aman's marks in CBSE XII = 410/500

Percentage of marks obtained by Aman = (410/500) × 100 = 82

Anish's marks in CBSE IX = 536/600

Percentage of marks obtained by Anish = (536/600) × 100 = 89.33

So, Anish's performance (89.33%) is better than Aman's (82%).

#### Page No 11.13:

#### Question 8:

Rahim obtained 60 marks out of 75 in Mathematics. Find the percentage of marks obtained by Rahim in Mathematics.

#### Answer:

Marks obtained by Rahim in mathematics = 60/75

Percentage of marks obtained by Rahim = (60/75) × 100 = 80

That is, 80%.

#### Page No 11.13:

#### Question 9:

In an orchard, $16\frac{2}{3}\%$ of the trees are apple trees. If the number of trees in the orchard is 240, find the number of other type of trees in the orchard.

#### Answer:

Let the number of apple trees be 'x'.

Number of trees in the orchard = 240

Number of apple trees = $16\frac{2}{3}$% of x

According to the given condition,

$16\frac{2}{3}$% of 240* = *x

⇒ ($\frac{50}{3}\xf7100$) × 240* = *x

⇒ $\frac{50\times 240}{3\times 100}$ = x

⇒ x = 40

Number of other types of trees = Total number of trees - number of apple trees = 240 - 40 = 200 trees

#### Page No 11.13:

#### Question 10:

Ram scored 553 marks out of 700 and Gita scored 486 marks out of 600 in science. Whose performance is better?

#### Answer:

Marks scored by Ram = 553/700

Percentage of marks scored by Ram = (553/700) × 100 = 0.79 × 100 = 79

Marks scored by Gita = 486/600

Percentage of marks scored by Gita = (486/600) × 100 = 0.81 × 100 = 81

Gita's performance (81%) is better than Ram's (79%).

#### Page No 11.13:

#### Question 11:

Out of an income of Rs 15000, Nazima spends Rs 10200. What per cent of her income does she save?

#### Answer:

Nazima's total income = Rs. 15000

Amount Nazima spends = Rs. 10200

Amount Nazima saves = Rs. (15000 - 10200) = Rs. 4800

Percentage of income Nazima saves = (4800/10200) × 100 = 480000/10200 = 32

Nazima saves 32% of her income.

#### Page No 11.13:

#### Question 12:

45% of the students in a school are boys. If the total number of students in the school is 880, find the number of girls in the school.

#### Answer:

Total number of students in the school = 880

Number of boys in the school = 45% of 880

= (45/100) × 880

= 39600/100 = 396

Number of girls in the school = 880 - 396 = 484

#### Page No 11.14:

#### Question 13:

Mr. Sidhana saves 28% of his income. If he saves Rs 840 pr month, find his monthely income.

#### Answer:

Let Mr. Sidhana's monthly income be *x.*

Monthly savings = Rs. 840

28% of *x = *Rs. 840

⇒ (28/100) × *x = *Rs. 840

⇒ 28*x* = Rs. 84000

⇒ *x* = Rs. (84000/28) = Rs. 3000

Mr. Sidhana's monthly income = Rs. 3000

#### Page No 11.14:

#### Question 14:

In an examination, 8% of the students fail. What percentage of the students pass? If 1650 students appeared in the examination, how many passed?

#### Answer:

Total number of students who appeared for the examination = 1650

Number of students who failed = 8% of 1650

= (8/100) ×1650

= (8 × 1650)/100

= 13200/100 = 132

Number of students who passed = 1650 - 132 = 1518

Percentage of students who passed = (1518/1650) × 100 = 0.92 × 100 = 92

That is, 92% of the students passed the examination.

#### Page No 11.14:

#### Question 15:

In an examination, 9% of the candidates passed and 46 failed. How many candidates appeared?

#### Answer:

Let the total number of candidates be *x.*

Number of candidates who failed = 46

Number of candidates who passed = 92% of *x *

According to the given condition,

92% of *x = x - *46

⇒ (92/100) *x = x - *46

⇒ 92*x** = *100*x** - *4600

⇒ -8*x** = - *4600

⇒ *x = *4600/8 =

Number of candidates who appeared for the examination = 575

#### Page No 11.14:

#### Question 1:

$\frac{2}{5}$ as a percent is

(a) 30%

(b) 35%

(c) 40%

(d) 45%

#### Answer:

$\frac{2}{5}=\frac{2}{5}\times \frac{100}{100}\phantom{\rule{0ex}{0ex}}=\frac{40}{100}\phantom{\rule{0ex}{0ex}}=40\%$

Hence, the correct option is (c).

#### Page No 11.14:

#### Question 2:

$\frac{5}{4}$ as a percent is

(a) 80%

(b) 125%

(c) 120%

(d) 130%

#### Answer:

$\frac{5}{4}=\frac{5}{4}\times \frac{100}{100}\phantom{\rule{0ex}{0ex}}=\frac{5\times 25}{100}\phantom{\rule{0ex}{0ex}}=\frac{125}{100}\phantom{\rule{0ex}{0ex}}=125\%$

Hence, the correct option is (b).

#### Page No 11.14:

#### Question 3:

The ratio 3 : 5 as a percent is

(a) 60%

(b) 50%

(c) 40%

(d) 80%

#### Answer:

$\frac{3}{5}=\frac{3}{5}\times \frac{100}{100}\phantom{\rule{0ex}{0ex}}=\frac{3\times 20}{100}\phantom{\rule{0ex}{0ex}}=\frac{60}{100}\phantom{\rule{0ex}{0ex}}=60\%$

Hence, the correct option is (a).

#### Page No 11.14:

#### Question 4:

12% as a fraction is

(a) $\frac{3}{25}$

(b) $\frac{4}{25}$

(c) $\frac{3}{20}$

(d) $\frac{6}{25}$

#### Answer:

$12\%=\frac{12}{100}\phantom{\rule{0ex}{0ex}}=\frac{12\xf74}{100\xf74}\phantom{\rule{0ex}{0ex}}=\frac{3}{25}$

Hence, the correct option is (a).

#### Page No 11.14:

#### Question 5:

$1\frac{1}{4}\%$ as a fraction is

(a) $\frac{1}{40}$

(b) $\frac{1}{60}$

(c) $\frac{1}{80}$

(d) $\frac{1}{70}$

#### Answer:

$1\frac{1}{4}\%=\frac{5}{4}\%\phantom{\rule{0ex}{0ex}}=\frac{5}{4}\times \frac{1}{100}\phantom{\rule{0ex}{0ex}}=\frac{1}{4\times 20}\phantom{\rule{0ex}{0ex}}=\frac{1}{80}$

Hence, the correct option is (c).

#### Page No 11.14:

#### Question 6:

Which of the following fractions is equivalent to 25% ?

(a) $\frac{1}{4}$

(b) $\frac{1}{5}$

(c) $\frac{1}{3}$

(d) $\frac{1}{2}$

#### Answer:

$25\%=\frac{25}{100}\phantom{\rule{0ex}{0ex}}=\frac{25\xf725}{100\xf725}\phantom{\rule{0ex}{0ex}}=\frac{1}{4}$

Hence, the correct option is (a).

#### Page No 11.14:

#### Question 7:

If 25% of *x* is 100, then *x* =

(a) 100

(b) 200

(c) 300

(d) 400

#### Answer:

$25\%\mathrm{of}x=100\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{25}{100}\times x=100\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{x}{4}=100\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{4\times x}{4}=4\times 100\phantom{\rule{0ex}{0ex}}\Rightarrow x=400$

Hence, the correct option is (d).

#### Page No 11.14:

#### Question 8:

If 8% of a number is 6, then the number is

(a) 96

(b) 60

(c) 96

(d) 75

#### Answer:

Let the required number be *x*.

$8\%\mathrm{of}x=6\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{8}{100}\times x=6\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{2x}{25}=6\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{2x\times 25}{25}=6\times 25\phantom{\rule{0ex}{0ex}}\Rightarrow 2x=150\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{150}{2}\phantom{\rule{0ex}{0ex}}\Rightarrow x=75$

Hence, the correct option is (d).

#### Page No 11.14:

#### Question 9:

If *x*% of 75 is 12, then *x* =

(a) 8

(b) 10

(c) 12

(d) 16

#### Answer:

Let the required number be *x*.

$x\%\mathrm{of}75=12\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{x}{100}\times 75=12\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{3x}{4}=12\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{3x\times 4}{4}=12\times 4\phantom{\rule{0ex}{0ex}}\Rightarrow 3x=48\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{48}{3}\phantom{\rule{0ex}{0ex}}\Rightarrow x=16$

Hence, the correct option is (d).

#### Page No 11.14:

#### Question 10:

If $\frac{5}{6}$ of 29% of *x *is 29, then *x* =

(a) 290

(b) 58

(c) 120

(d) 100

#### Answer:

Let the required number be *x*.

$\frac{5}{6}of29\%\mathrm{of}x=29\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{5}{6}\left(\frac{29}{100}\times x\right)=29\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{29x}{120}=29\phantom{\rule{0ex}{0ex}}\Rightarrow 29x=29\times 120\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{29\times 120}{29}\phantom{\rule{0ex}{0ex}}\Rightarrow x=120$

Hence, the correct option is (c).

#### Page No 11.14:

#### Question 11:

What percent of $\frac{2}{7}$ is $\frac{1}{35}$?

(a) 25%

(b) 20%

(c) 15%

(d) 10%

#### Answer:

Let the required number be *x*.

$x\%\mathrm{of}\frac{2}{7}=\frac{1}{35}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{x}{100}\times \frac{2}{7}=\frac{1}{35}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{x}{350}=\frac{1}{35}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{350\times x}{350}=\frac{1\times 350}{35}\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{350}{35}\phantom{\rule{0ex}{0ex}}\Rightarrow x=10$

Hence, the correct option is (d).

#### Page No 11.15:

#### Question 12:

If *x* = 100, then 120% of *x* is

(a) 125

(b) 115

(c) 120

(d) 110

#### Answer:

120% of *x* = $\frac{120}{100}\times 100=120$

Hence, the correct option is (c).

#### Page No 11.15:

#### Question 13:

40% of 150 + 60% of 150 =

(a) 200

(b) 150

(c) 250

(d) 180

#### Answer:

$40\%\mathrm{of}150=\frac{40}{100}\times 150\phantom{\rule{0ex}{0ex}}=60\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}60\%\mathrm{of}150=\frac{60}{100}\times 150\phantom{\rule{0ex}{0ex}}=90$

Therefore, 40% of 150 + 60% of 150 = 60 + 90 = 150.

Hence, the correct option is (b).

#### Page No 11.15:

#### Question 14:

50% of 150 + 70% of 300 =

(a) 295

(b) 285

(c) 265

(d) 275

#### Answer:

$50\%\mathrm{of}150=\frac{50}{100}\times 150\phantom{\rule{0ex}{0ex}}=75\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}70\%\mathrm{of}300=\frac{70}{100}\times 300\phantom{\rule{0ex}{0ex}}=210$

Therefore, 50% of 150 + 70% of 300 = 75 + 210 = 285.

Hence, the correct option is (b).

#### Page No 11.15:

#### Question 15:

55% of 1000 ÷ 60% of 2000 =

(a) $\frac{11}{24}$

(b) $\frac{12}{25}$

(c) $\frac{13}{24}$

(d) $\frac{14}{25}$

#### Answer:

$55\%\mathrm{of}1000=\frac{55}{100}\times 1000\phantom{\rule{0ex}{0ex}}=550\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}60\%\mathrm{of}2000=\frac{60}{100}\times 2000\phantom{\rule{0ex}{0ex}}=1200\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathrm{Therefore},55\%\mathrm{of}1000\xf760\%\mathrm{of}2000=\frac{550}{1200}=\frac{550\xf750}{1200\xf750}=\frac{11}{24}.\phantom{\rule{0ex}{0ex}}$

Hence, the correct option is (a).

#### Page No 11.15:

#### Question 16:

If *x*% of 2000 = 600, then *x* =

(a) 60

(b) 30

(c) 40

(d) 50

#### Answer:

$x\%\mathrm{of}2000=600\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{x}{100}\times 2000=600\phantom{\rule{0ex}{0ex}}\Rightarrow 20x=600\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{600}{20}\phantom{\rule{0ex}{0ex}}\Rightarrow x=30$

Hence, the correct option is (b).

#### Page No 11.15:

#### Question 17:

If *x*% of $\frac{12}{5}\mathrm{is}\frac{18}{25}$, then *x* =

(a) 30

(b) 40

(c) 72

(d) 50

#### Answer:

$x\%\mathrm{of}\frac{12}{5}=\frac{18}{25}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{x}{100}\times \frac{12}{5}=\frac{18}{25}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{12x\times 500}{500}=\frac{18\times 500}{25}\phantom{\rule{0ex}{0ex}}\Rightarrow 12x=18\times 20\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{18\times 20}{12}\phantom{\rule{0ex}{0ex}}\Rightarrow x=30$

Hence, the correct option is (a).

#### Page No 11.15:

#### Question 18:

The value of 30% of 60% of 200 is

(a) 23

(b) 24

(c) 18

(d) 36

#### Answer:

$60\%\mathrm{of}200=\frac{60}{100}\times 200\phantom{\rule{0ex}{0ex}}=120\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}30\%\mathrm{of}60\%\mathrm{of}200=\frac{30}{100}\times 120\phantom{\rule{0ex}{0ex}}=36$

Hence, the correct option is (d).

#### Page No 11.15:

#### Question 19:

If $\frac{2}{5}$ of 50% of *x* is 10,then *x* =

(a) 100

(b) 50

(c) 25

(d) 80

#### Answer:

$\frac{2}{5}\mathrm{of}50\%\mathrm{of}x=10\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{2}{5}\times \frac{50}{100}\times x=10\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{x}{5}=10\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{x\times 5}{5}=10\times 5\phantom{\rule{0ex}{0ex}}\Rightarrow x=50$

Hence, the correct option is (b).

#### Page No 11.15:

#### Question 20:

If $\frac{4}{7}$ of 49% of *x* is 21,then *x* =

(a) 125

(b) 98

(c) 84

(d) 75

#### Answer:

$\frac{4}{7}\mathrm{of}49\%\mathrm{of}x=21\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{4}{7}\times \frac{49}{100}\times x=21\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{7x}{25}=21\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{7x\times 25}{25}=21\times 25\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{21\times 25}{7}\phantom{\rule{0ex}{0ex}}\Rightarrow x=75$

Hence, the correct option is (d).

#### Page No 11.15:

#### Question 21:

Which of the following fractions is equivalent to 12.5% ?

(a) $\frac{1}{8}$

(b) $\frac{1}{6}$

(c) $\frac{1}{5}$

(d) $\frac{1}{12}$

#### Answer:

$12.5\%=\frac{12.5}{100}\phantom{\rule{0ex}{0ex}}=\frac{125}{1000}\phantom{\rule{0ex}{0ex}}=\frac{125\xf725}{1000\xf725}\phantom{\rule{0ex}{0ex}}=\frac{5}{40}\phantom{\rule{0ex}{0ex}}=\frac{5\xf75}{40\xf75}\phantom{\rule{0ex}{0ex}}=\frac{1}{8}$

Hence, the correct option is (a).

#### Page No 11.15:

#### Question 22:

Ravish saved 55% of his income. If his income is ₹11000, then his expenditure is

(a) ₹6050

(b) ₹7450

(c) ₹4950

(d) ₹3550

#### Answer:

Savings of Ravish = 55% of ₹11000

Expenditures of Ravish = 45% of ₹11000

= $\frac{45}{100}\times 11000$

= ₹4950

Hence, the correct option is (c).

#### Page No 11.15:

#### Question 23:

If 35% of a number added to 39 is the number itself, the number is

(a) 60

(b) 65

(c) 75

(d) 105

#### Answer:

Let the required number be *x*.

According to the question,

$35\%\mathrm{of}x+39=x\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{35}{100}\times x+39=x\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{35x\times 100}{100}=\left(x-39\right)\times 100\phantom{\rule{0ex}{0ex}}\Rightarrow 35x=100x-3900\phantom{\rule{0ex}{0ex}}\Rightarrow 100x-35x=3900\phantom{\rule{0ex}{0ex}}\Rightarrow 65x=3900\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{3900}{65}\phantom{\rule{0ex}{0ex}}\Rightarrow x=60$

Hence, the correct option is (a).

#### Page No 11.15:

#### Question 24:

On increasing the salary of a man by 25%, it becomes ₹20,000. What was his original salary?

(a) ₹15000

(b) ₹16000

(c) ₹18000

(d) ₹25000

#### Answer:

Let the original salary of the man be *x*.

According to the question,

$x+25\%\mathrm{of}x=20000\phantom{\rule{0ex}{0ex}}\Rightarrow x+\frac{25}{100}\times x=20000\phantom{\rule{0ex}{0ex}}\Rightarrow x+\frac{x}{4}=20000\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{4x+4}{4}=20000\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{5x}{4}\times 4=20000\times 4\phantom{\rule{0ex}{0ex}}\Rightarrow 5x=80000\phantom{\rule{0ex}{0ex}}\Rightarrow x=\frac{80000}{5}\phantom{\rule{0ex}{0ex}}\Rightarrow x=16000$

Therefore, Original salary of the man is ₹16000.

Hence, the correct option is (b).

#### Page No 11.15:

#### Question 25:

Rohit scored 180 marks in the first test and 150 marks in the second test. The maximum marks in each test is 200. What is the decrease in his performance in percentage points?

(a) 20%

(b) 15%

(c) 25%

(d) 23%

#### Answer:

Marks scored in first test = 180

Marks scored in second test = 150

Maximum marks = 200

Decrease in marks = 180 − 150 = 30

Decrease in performance in percentage = $\frac{30}{200}\times 100=15\%$

Hence, the correct option is (b).

#### Page No 11.3:

#### Question 1:

Express each of the following per cents as fractions in the simplest forms:

(i) 45%

(ii) 0.25%

(iii) 150%

(iv) $6\frac{1}{4}\%$

#### Answer:

(i) 45% = 45/100 = 9/20

(ii) 0.25% = 0.25/100 = 25/10000 = 5/2000 = 1/400

(iii) 150% = 150/100 = 15/10 = 3/2

(iv) $6\frac{1}{4}\%=\frac{25}{4}\xf7100=\frac{25}{100\times 4}=\frac{1}{16}$

#### Page No 11.3:

#### Question 2:

Express each of the following fractions as a per cent:

(i) $\frac{3}{4}$

(ii) $\frac{53}{100}$

(iii) $1\frac{3}{5}$

(iv) $\frac{7}{20}$

#### Answer:

(i) $\left(\frac{3}{4}\times 100\right)\%=75\%$

(ii) $\left(\frac{53}{100}\times 100\right)\%=53\%$

(iii) $1\frac{3}{5}=\left(\frac{8}{5}\times 100\right)\%=160\%$

(iv) $\left(\frac{7}{20}\times 100\right)\%=35\%$

#### Page No 11.4:

#### Question 1:

Express each of the following ratios as per cents:

(i) 4 : 5

(ii) 1 : 5

(iii) 11 : 125

#### Answer:

$\left(i\right)4:5=\frac{4}{5}=\left(\frac{4}{5}\times 100\right)\%=80\%\phantom{\rule{0ex}{0ex}}\left(ii\right)1:5=\frac{1}{5}=\left(\frac{1}{5}\times 100\right)\%=20\%\phantom{\rule{0ex}{0ex}}\left(iii\right)11:125=\frac{11}{125}=\left(\frac{11}{125}\times 100\right)\%=8.8\%$

#### Page No 11.4:

#### Question 2:

Express each of the following per cents as ratios in the simplest forms:

(i) 2.5%

(ii) 0.4%

(iii) $13\frac{3}{4}\%$

#### Answer:

(i) 2.5% = 2.5/100 = 25/1000 = 5/200 = 1/40

(ii) 0.4% = 0.4/100 = 4/1000 = 1/250

(iii) $13\frac{3}{4}=\frac{55}{4\times 100}=\frac{11}{80}$

#### Page No 11.5:

#### Question 1:

Express each of the following per cents as decimals:

(i) 12.5%

(ii) 75%

(iii) 128.8%

(iv) 0.05%

#### Answer:

(i) 12.5% = 12.5/100 = 125/1000 = 0.125

(ii) 75% = 75/100 = 0.75

(iii) 128.8% = 128.8/100 = 1288/1000 = 1.288

(iv) 0.05% = 0.05/100 = 5/10000 = 0.0005

#### Page No 11.5:

#### Question 2:

Express each of the following decimals as a per cent:

(i) 0.004

(ii) 0.24

(iii) 0.02

(iv) 0.275

#### Answer:

(i) 0.004 = (0.004 × 100)% = 0.4%

(ii) 0.24 = (0.24 × 100 )% = 24%

(iii) 0.02 = (0.02 × 100)% = 2%

(iv) 0.275 = (0.275 × 100)% = 27.5%

#### Page No 11.5:

#### Question 3:

Write each of the following as whole numbers or mixed numbers:

(i) 136%

(ii) 250%

(iii) 300%

#### Answer:

(i) 136% = 136/100 = 34/25

(ii) 250% = 250/100 = 5/2

(iii) 300% = 300/100 = 3

#### Page No 11.7:

#### Question 1:

Find each of the following:

(i) 7% of Rs 7150

(ii) 40% of 400 kg

(iii) 20% of 15.125 litres

(iv) $3\frac{1}{3}\%\mathrm{of}90\mathrm{km}$

(v) 2.5% of 600 metres

#### Answer:

(i) 7% of Rs. 7150 = (7/100) × 7150 = 50050/100 = Rs. 500.50

(ii) 40% of 400 kg = (40/100) × 400 = 16000/100 = 160 kg

(iii) 20% of 15.125 litres = (20/100) × 15.125 = 302.5/100 = 3.025 litres

(iv) $3\frac{1}{3}\%=\frac{10}{3\times 100}\times 90=3\text{km}$

(v) 2.5% of 600 metres = (2.5/100) × 600 = 1500/100 = 15 metres

#### Page No 11.7:

#### Question 2:

Find the number whose $12\frac{1}{2}\%$ is 64.

#### Answer:

Let the number be x.

$12\frac{1}{2}\%\text{ofx}=64\phantom{\rule{0ex}{0ex}}\frac{25}{2}\xf7100\times \text{x}=64\phantom{\rule{0ex}{0ex}}\frac{25\times \text{x}}{2\times 100}=64\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}25\times \text{x}=64\times 2\times 100\phantom{\rule{0ex}{0ex}}x=\frac{\mathrm{64\times 2\times 100}}{25}=512$

#### Page No 11.7:

#### Question 3:

What is the number, $6\frac{1}{4}\%$ of which is 2?

#### Answer:

Let the number be x.

$6\frac{1}{4}\xf7100\text{ofx}=2\phantom{\rule{0ex}{0ex}}\frac{25}{4}\xf7100\times \text{x}=2\phantom{\rule{0ex}{0ex}}\frac{25\times \text{x}}{4\times 100}=2\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}25\times \text{x}=2\times 4\times 100\phantom{\rule{0ex}{0ex}}x=\frac{2\times 4\times 100}{25}=32$

#### Page No 11.7:

#### Question 4:

If 6 is 50% of a number, what is that number?

#### Answer:

Let the number be x.

50% of *x = *6

⇒ (50/100) *× x = *6

⇒ *x = *600/50

⇒ *x = *12

So, the number is 12.

#### Page No 11.9:

#### Question 1:

What per cent of

(i) 24 is 6?

(ii) Rs 125 is Rs 10?

(iii) 4 km is 160 metres?

(iv) Rs 8 is 25 paise

(v) 2 days is 8 hours?

(vi) 1 litre is 175 ml?

#### Answer:

Let the number be *x*.

(i) 24% of *x* = 6

⇒ (24/100) × *x = *6

⇒ *x = *600/24 = 25%

(ii) 125% of *x * = 10

⇒ (125/100) × *x = *10

⇒* x = *1000/125 = 8%

(iii) 4 km = 4000 metres (1 km = 1000 m)

4000% of *x = *160

⇒ (4000/100) × x = 160

*⇒ x* = 16000/4000 = 4%

(iv) Rs. 8 = 800 paise (Re. 1 = 100 paise)

800% of *x = * 25

⇒ (800/ 100) × *x = *25

⇒ *x* = 2500/800 = 25/8 = 3.125%

(v) 2 days = 2 × 24 = 48 (1 day = 24 hours)

48% of *x = *8

⇒ (48/100) × *x = *8

⇒ *x = *800/48 = 100/6 = 16.66%

(vi) 1 litre = 1000 ml

1000% of *x = *175

⇒ (1000/100) × *x = *175

⇒ *x = *17500/1000 = 175/10 = 17.5%

#### Page No 11.9:

#### Question 2:

What per cent is equivalent to $\frac{3}{8}$?

#### Answer:

Let the percentage equivalent to 3/8 be *x*.

Then, *x*% = $\frac{3}{8}$

⇒ *x/*100 = $\frac{3}{8}$

⇒ *x = *$\frac{3\times 100}{8}=37.5$

Therefore, 3/8 = 37.5%.

#### Page No 11.9:

#### Question 3:

Find the following:

(i) 8 is 4% of which number?

(ii) 6 is 60% of which number?

(iii) 6 is 30% of which number?

(iv) 12 is 25% of which number?

#### Answer:

Let the number be x.

(i)* *4% of *x * = 8

⇒ (4/100) × *x* = 8

⇒ *x = *800/4 = 200

(ii) 60% of *x = *6

⇒ (60/100) × *x * = 6

⇒ *x = *600/60 = 10

(iii) 30% of *x = *6

⇒ (30/100) × *x = *6

⇒ *x = *600/30 = 20

(iv) 25% of *x = *12

⇒ (25/100) × *x = *12

⇒ *x = *1200/25 = 48

#### Page No 11.9:

#### Question 4:

Convert each of the following pairs into percentages and find out which is more?

(i) 25 marks out of 30, 35 marks out of 40.

(ii) 100 runs scored off 110 balls, 50 runs scored off 55 balls.

#### Answer:

(i) 25 marks out of 30

⇒ (25/30) × 100 = 2500/30 = 83.33%

35 marks out of 40

⇒ (35/40) × 100 = 3500/40 = 87.5%

87.5% is greater than 83.33%.

(ii) 100 runs scored off 110 balls

⇒ (100/110) × 100 = 10000/110 = 90.90%

50 runs scored off 55 balls

⇒ (50/55) × 100 = 5000/55 = 90.90%

Both percentages are equal.

#### Page No 11.9:

#### Question 5:

Find 20% more than Rs 200.

#### Answer:

20% more than 200 means 20% of 200 plus 200.

That is, {(20/100) × 200} + 200 = (4000/100) + 200 = 40 + 200 = 240.

#### Page No 11.9:

#### Question 6:

Find 10% less than Rs 150.

#### Answer:

10% less than Rs. 150 means 150 minus 10% of 150.

That is, 150 - {(10/100) × 150} = 150 - (1500/100) = 150 - 15 = Rs. 135.

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