EXERCISE:7.1
Question 1
i) $25 \%=\frac{25}{100}=\frac{1}{4}$
ii) $150 \%=\frac{150}{100}=\frac{3}{2}$.
iii) $7 \frac{1}{2} \%=\frac{15}{2} \%=\frac{15 / 2}{100}=\frac{15}{2 \times 100}=\frac{3}{40}$
iv) $33 \frac{1}{3} \%=\frac{100}{3} \%=\frac{100 / 3}{100}=\frac{100}{3 \times 100}=\frac{1}{3} .$
Question 2
i) $\frac{1}{8}=\left(\frac{1}{8} \times 100\right) \%=12.5 \%$
ii) $\frac{5}{4}=\left(\frac{5}{4} \times 100\right) \%=125 \%$
iii) $\frac{9}{16}=\left(\frac{9}{16} \times 100\right) \%=56 \frac{1}{4} \%$
iv) $\frac{3}{7}=\left(\frac{3}{2} \times 100\right) \%=42 \frac{6}{7} \%$
v) $\frac{11}{15}=\left(\frac{11}{15} \times 100\right) \%=73 \frac{1}{3} \%$
vi) $\frac{13}{8}=\frac{11}{8}=\left(\frac{11}{8} \times 100\right) \%=137 \frac{1}{2} \%$
Question 3
i) Given 6 students out of 40 students in a class are absent
percentage of students are absent $=\frac{6}{40} \times 100 \%$
=15%
ii) Given, Antony secured 384 marks out of 500 maiks.
$\therefore$ percentage of marks secured $=\left(\frac{384}{500} \times 100\right) \%$
$=76.8 \%$
iii) Given , A shop has 500 shirts
Out of 500 shirts , 15 are defective
Now, percentage of shirts are defective = $\left(\frac{15}{500} \times 100\right) \%$
=3%
iv) Given,
Vani has 20 gold bangels
Also she has 10 silver bangles
Now, Total number of bangles = 20+ 10 = 30 bangles
∴ percentage of gold bangles = ($\left.\frac{20}{30} \times 100\right) \%$
=66.67 %
$\begin{aligned} \text { percentage of Silver bangles } &=\left(\frac{10}{30} \times 100\right) \% \\ &=33.34 \% \end{aligned}$
v) Total number of voters = 120
Out of 120 , 90 of them voted
Then out of 120, votes did not vote = 120-90=30
ஃPercentage of voters did not vote = $\frac{30}{120} \times 100 \%$
=$25 \%$
Question 4
i) Shaded part $=\frac{3}{4}$
percentage of Shaded part $=\left(\frac{3}{4} \times 100\right) \%$
$=75 \%$
ii) Shaded part $=\frac{2}{6}=\frac{1}{3}$
percentage of Shaded part $=\left(\frac{1}{3} \times 100\right) \%$
$=33.34 \%$
iii) Shaded part $=\frac{5}{8}$
percentage of shaded part $=\left(\frac{5}{8} \times 100\right) \%=62.5 \%$
Question 5
i) $14 \%=\frac{14}{100}=\frac{7}{50} .$
ii) $1 \frac{3}{4} \%=\frac{7}{4} \%=\frac{7}{4 \times 100}=\frac{7}{400} .$
iii) $33 \frac{1}{3} \%=\frac{100}{3} \%=\frac{100}{3 \times 100}=\frac{1}{3} .$
iv) $37.5 \%=\frac{37.5}{100}=\frac{375}{1000}=\frac{3}{8} .$
Question 6
i) $\frac{5}{4}=\left(\frac{5}{4} \times 100\right) \%=125 \%$
ii) $\frac{1}{1}=\left(\frac{1}{1} \times 100\right) \%=100 \%$
iii) $\frac{2}{3}=\left(\frac{2}{3} \times 100\right) \%=66.67 \%$
iv) $\frac{9}{16}=\left(\frac{9}{16} \times 100\right) \%=56.25 \%$
Question 7
Given alloy consists of 7 parts of zinc and 33 parts of copper
Total alloy contains = 33+ 7 = 40
ஃ percentage of copper in alloy = $\left(\frac{33}{40} \times 100\right) \%$
=$82.5 \%$
Question 8
Given , Calcium, carbon and sand in the ratio 12:3:10
Sum of ratio = 12+ 3+ 10 = 25
Percentage of carbon in the chalk = ($\frac{3}{25} \times 100$) % =12%
Question 9
Given Total money = Rs 2500
It is divided among Ravi, Raju and Roy
Out of total money , ravi gets two parts
Raju gets three parts
Roy gets five parts
Total no. of parts = 2+ 3+ 5= 10
Ravi get money = Rs $\frac{2}{10} \times 2500$
=Rs 500
$\begin{aligned} \text { Raju gets money } &=3 \frac{3}{10} \times 2500 \\ &= 750 rs. \\ \text { Roy gets money } &= \frac{5}{10} \times 2500 \\ &= 1250 rs . \end{aligned}$
Percentage of Ravi get money $\begin{aligned} &=\left(\frac{500}{2500} \times 100\right) \% \\ &=20 \% \end{aligned}$
$\begin{aligned} \text { percentage of Raju gets money } &=\left(\frac{750}{2500} \times 100\right) \% \\ &=30 \% \end{aligned}$
$\begin{aligned} \text { Percentage of Roy geT money } &=\left(\frac{1250}{2500} \times 100\right) \% \\ &=50 \% \end{aligned}$
Question 10
i) $28 \%=\frac{28}{100}=0.28 .$
ii) $3 \%=\frac{3}{100}=0.03$
iii) $0.44 \%=\frac{0.44}{100}=0.0044$
iv) $37 \frac{1}{2} \%=\frac{75}{2} \%=\frac{75}{2 \times 100}=0.335$
Question 11
i) $0.65=\frac{65}{100}=\left(\frac{65}{100} \times 100\right) \%=65 \%$
ii) $0.90=\frac{90}{100}=\left(\frac{90}{100} \times 100\right) \%=90 \%$
iii) $2.1=\frac{21}{10}=\left(\frac{21}{10} \times 100\right) \%=210 \%$
iv) $0.02=\frac{2}{100}=\left(\frac{2}{100} \times 100\right) \%=2 \%$
Question 12
i) Given percentage of students in a class are girls = 42%
Actual percentage of students in a class will be 100%
Percentage of students in a class are boys = (100-42)% =58%
ii) A basket have full of apples , oranges and mangoes
Percentage of apples = 50 %
Percentage of oranges = 30%
Percentage of total oranges , apples and mangoes = 100 %
ஃNow percentage of mangoes = [$100-(50+30)$]%
$=[100-80] %$
$=20 %$
EXERCISE:7.2
Question 1
i) $15 %$ of $250=\frac{15}{100} \times 250=\frac{3}{20} \times 250=375$
ii) $25\% $ of 120 litres $=\frac{25}{100} \times 120=\frac{1}{4} \times 120=30$.
iii) $1 \%$ of 1 hour $=\frac{1}{100} \times 3600 \mathrm{sec}=36$ seconds.
iv) $75 \%$ of $\mathrm{Kg}=\frac{75}{100} \times 1000 \mathrm{~g}=\frac{3}{4} \times 1000 \mathrm{gr} \mathrm{ms}=750 \mathrm{~g}$
V) $120 \%$ of $\ 250=\frac{120}{100} \times 250$=Rs 300
vi) $0.6 \%$ of $2 \mathrm{Km}=\frac{0.6}{100} \times 2000 \mathrm{~m}=12 \mathrm{~m}$
Question 2
Given , 8% children of a class like getting wet = 25
Now , children like getting wet=$\frac{8}{100} \times 25$
=$\frac{2}{25} \times 25$
=2
Question 3
Given,
Out of 20 in the fridge, Vasundara ate = 3 ice creams
Percentage of icecreams , she ate = $\frac{3}{20} \times 100 \%$
=15 %
Question 4
i) Required percentage $=\left(\frac{20}{50} \times 100\right) \%=\frac{200}{5} \%=40 \%$
ii) Required percentage $=\left(\frac{60}{40} \times 100\right) \%=\frac{300}{2} \%=150 \%$
iii) Required percentage $=\left(\frac{90cm}{4 \cdot 5 m} \times 100\right) \%=\left(\frac{90}{4.5 \times 100} \times 100\right) \%$
$=\left(\frac{90}{450} \times 100\right) \%$
$=\frac{100}{5} \%$
$=20 \%$
iv) $5.6 \mathrm{~kg}=5.6 \times 1000 \mathrm{~g}=5600 \mathrm{~g}$
$\begin{aligned} \text { Required Percentage }=\left(\frac{3509}{56008} \times 100\right) \% &=\frac{350}{56} \% \\ &=6.25 \% \end{aligned}$
Question 5
i) 12 of $80=\left(\frac{12}{80} \times 100\right) \%=\frac{120}{8} \%=15 \%$
ii) $\quad$ 4 rupees $=4 \times 100$ paide $=400$ paise
25 paise of 400 paise = $\left(\frac{25}{400} \times 100\right) \%=\frac{25}{4} \%=6.25 \%$
iii) $2 \mathrm{~kg}=2 \times 1000 \mathrm{~g}=2000 \mathrm{~g}$
$300 \mathrm{~g}$ of $200 \mathrm{~g}=\left(\frac{300}{2000} \times 100\right) \%=\frac{30}{2} \%=15 \%$
Question 6
Percentage increase $=\left(\frac{\text { intrease in value }}{\text { Original value }} \times 100\right) \%$
A school team won 4 games last years, and this year the team won 6 games.
Increase in the games won = 6-4=2
ஃ percentage increase = $\begin{aligned} &( \left.\frac{2}{4} \times 100\right) \% \\ & \frac{100}{2} \\=& 50 \% \end{aligned}$
Question 7
Original price = Rs 80
Decrease in price = Rs 80 - Rs 60
= Rs 20
Percentage Decrease $=\left[\frac{D ecr e a s e \text { in value }}{\text { original value }} \times 100\right] \%$
$=\left[\frac{20}{80} \times 100\right] \%$
$=\frac{100}{4} \%$
$=25 \%$
Question 8
In Childhood , petrol price was = Rs 1 per litre
Now the price of petrol was = Rs 65 per litre
Increase in the Value of price = Rs 65 - Rs 1
= Rs 64
ஃ Percentage increase = $\left(\frac{64}{1} \times 100\right) \%$
$6400 \%$
Question 9
Last years, the cost of basmati rice= Rs 40 kg
Also , percentage increase = 20 %
∴This price , this year will be increased by
= $\frac{20}{100} \times 40$
=8 a $\mathrm{kg}$
∴ $\begin{aligned} \therefore \text { The price of Bamati rice, tis year } &=40+8 \\ &= ₹ 48 \text { kg. } \end{aligned}$
Question 10
Number of students took exam = 300
Percentage failed = 28%
Number of students failed $=\frac{28}{100} \times 300$
=84
∴ Now , the number of students passed= 300- 84
=216
Question 11
In a constituency, number of voters = 15,000
Percentage of voters who voted = 60%
∴ Number of votes who voted = $\frac{60}{100} \times 15000$
=9000
Question 12
Length of a flag pole painted green = 20%
Painted yellow = 455
Remaining painted red = 100-(20+ 45)
=100-65
= 35%
Total length of pole = 18m
Length of pole painted red =$\frac{35}{100} \times 18m$
=6.3m
Question 13
A chalk contains , calcium = 10%
Carbon = 3%
Oxygen = 12%
and the remaining is sand = 100- (10+3+12)
= 100-25
= 75%
Amount of carbon in $2 \frac{1}{2}$ kg chalk $=\frac{3}{100} \times \frac{5}{2} \times 1000 \mathrm{~g}$ = 75g
Amount of Calcium in $2 \frac{1}{2} \mathrm{~kg} \ chalk \mathrm{}=\frac{10}{100} \times \frac{5}{2} \times 1000 \mathrm{~g}$ = 250g
$\begin{aligned} \text { Amount of } \text { Sand } &=\frac{75}{100} \times \frac{5}{2} \mathrm{~kg} \\ &=1.875 \mathrm{~kg} \end{aligned}$
Question 14
i) $25 \%$ of $x$ is $9 \Rightarrow \frac{25}{100} \times x=9$
$\frac{x}{4}=9$
$x=4 \times 9$
$x=36$
ii) $75 \%$ of $x$ is $15 \Rightarrow \frac{75}{100} \times x=15$
$\frac{3 x}{4}=15$
$x=\frac{15 \times 4}{3}$
$x=20$
iii) $12 \%$ of it is Rs 1080
$\begin{aligned} \Rightarrow \frac{12}{100} \times x &=1080 \\ x &=\frac{1080 \times 100}{12} \\ x &=9000 . \end{aligned}$
iv) $8 \%$ of it is 40 litr $\Rightarrow \frac{8}{100} \times x=40$
$x=\frac{40 \times 100}{8}$
$x=500$
Question 15
Mohini Saved salary =Rs 400
percentage Saved $=10 \%$ of total salary
i.e $\frac{10}{100} \times x=400$
$x=\frac{400 \times 100}{10}$
$x=4000$
$\therefore$ Salary =Rs 4000
Question 16
Number of good apples in basket = 42
percentage of the apples in a basket go bad = 16%
Remaining , percentage of apples go good = 100- 16= 84%
Let Total no of apples be x
i.e 84% of x = 42
$\frac{84}{100} \times x=42$
$x=\frac{42 \times 100}{84}$
$x=50$
∴ Total number of apples = 50
Question 17
Varun got secured marks = 251 marks
and got failed by 19 marks
If he gets passed, then he will get = 251+19= 270 marks
percentage of marks to get pass = 45%
Let maximum marks be 'x'
i.e 45% of x = 270
$\begin{aligned} \frac{45}{100} \times x &=270 \\ x &=\frac{270 \times 100}{45} \\ x &=600 \end{aligned}$
∴ Maximum marks $=600$
Question 18
In a rainy day , percentage of students
present in a school = 94%
Then percentage of students absent = 100- 94%
= 6%
Also given , number of students absent on that
day = 174
Let total strength of school be x
i,e
$\begin{aligned} 6 \% \text { of } x &=134 . \\ \frac{6}{100} \times x &=174 \\ x &=\frac{174 \times 100}{6} \\ x &=2900 . \end{aligned}$
Total strength of school = 2900
Question 19
Percentage of population in a town are men = 40%
Those are women = 39%
Then percentage of population are children = 100-(39+40)
= 100-79
Number of children - 12,600
Let the total population be 'x '
i.e 21% of x = 12,600
$\begin{aligned} \frac{21}{100} \times x &=12,600 \\ x &=\frac{12,600 \times 100}{21} \\ x&=60,000 \end{aligned}$
∴ Now the number of men = 40% of total
$=\frac{40}{100} \times 60,000$
$=24,000$
Question 20
Price of watch is increased by 15%
Increase in price is Rs 90
percentage increase = $\frac{\text { Increase in value }}{\text { original value }} \times 100$
∴ i.e $15=\frac{90}{\text { original value }} \times 100$
$\begin{aligned} \therefore \text { original price } &=\frac{90 \times 100}{15} \\ \text { original price } &=2600 \end{aligned}$
Question 21
i)Let the original number be x
Increase in the number = 30% of x $=\frac{30}{100} \times x=\frac{3 x}{10}$
$\therefore$ New number $=x+\frac{3 x}{10}$
According to given Condition, $x+\frac{3 x}{10}=39$
$\begin{aligned} 10 x+3 x=39 \times 10 \Rightarrow 13 x &=390 \\ x &=\frac{390}{13}=30 \end{aligned}$
Hence , the original number is 30
ii) Let the original number be x
Decrease in number = 8% of x = $\frac{8}{100} \times x=\frac{2 x}{25}$
∴New number = $x-\frac{2 x}{25}$
Accoding to given information, $x-\frac{2 x}{25}=506$.
$25 x-2 x=506 \times 25$
$23 x=506 \times 25$
$x=\frac{506 \times 25}{23}$
$x=550$
Hence, the original number is 550
Question 22
Percentage reduced = 7%
Let the original number be x
Decreased in number = 7% of x =$\frac{7}{100} \times x=\frac{7 x}{100}$
∴ New number = $x-\frac{7 x}{100}=\frac{93 x}{100}$.
According to given , $\frac{93 x}{100}=165$
$x=\frac{465 \times 100}{93}$
$x=500$
∴ Original price = Rs 500
EXERCISE:7.3
Question 1
Cost price =Rs 60, selling price =₹ 874
Profit = Selling price - cost price
= 8 74- 760
= Rs 114
profit percentage = $\left(\frac{p r of i t}{c \cdot p} \times 100\right) \%$
$=\left(\frac{114}{760} \times 100\right) \%$
$=15 \%$
Question 2
Cost price =Rs 2500 ; selling price = Rs 2300
Loss $=$ cost price - selling price
= Rs 2500- Rs 2300
= Rs 200
Loss percent = ($\frac{\text { Loss }}{\text { C.P }} \times 100$)
$\begin{aligned}=&\left(\frac{200}{2500} \times 100\right) \cdot \% \\=8 \% . \end{aligned}$
Question 3
i) Cost price = Rs 250 ; Selling price = Rs 325
As S.p >C.P , Profit = S.P - C.p
=325-250
=Rs 75
profit percent $=\left(\frac{\text { profit }}{c \cdot p} \times 100\right) \%$
$=\left(\frac{75}{250} \times 100\right) \% .$
$=30 \%$
ii) Cost price = Rs 250 , Selling price = Rs 150
As C.P >S.P , Loss = C.P -S.P
=250- 150
= Rs 100
Loss percent $\left.=\frac{\text { Loss }}{C \cdot \rho} \times 100\right) \%$.
$=\left(\frac{100}{250} \times 100\right) \%$
$=40 \%$
Question 4
1st offer :
Cost price = Rs 4800
Profit = $13 \frac{1}{3} \%$ of Cost price = $\frac{40}{3} \times \frac{1}{100} \times 4800$
=640
Selling price = 480+ 640 i.e Cost price +profit = Rs 25440
2nd offer:
Cost price = Rs 3640
Loss = 15 % of cost price = $=\frac{15}{100} \times 3640$
=Rs 546
$\begin{aligned} \text { Selling price } &=\text { cost price - Loss } \\ &=3640-546 \\ &= 3094 rs. \end{aligned}$
Selling price of 1st and 2nd offer = 5440+ 3094
= Rs 8440
As S.P > C.P , He always get gain
i.e Gain = S.P - C.P
= 8534- 8440
= Rs 94
Question 5
cost price of 24 Tables $=24 \times 450$
= Rs 10,800
$\begin{aligned} \text { Selling price of } 16 \text { of them } &=16 \times 600 \\ &=9600 \end{aligned}$
Remaining i.e 24-16 =8 were sold
i.e now s.p of 8 tables = 8 $\times $ 400
= 3200
∴ Total selling price = 9600+ 3200
= 1,2800
As S.P > C.P there is always a gain
Gain = S.p - C.P
12,800- 10,800
= Rs 2000
Question 6
Selling price = Rs 810 ;$ profit =Rs 60
$\begin{aligned} \text { As } \text { profit } &=S \cdot p-c \cdot p \\ c \cdot p &=s \cdot p-\text { profit } \\ &=810-60 \end{aligned}$
Cost price =Rs 750
$\begin{aligned} \text { profit percent } &=\left(\frac{\text { profit }}{c \cdot p} \times 100\right) \% \\ &=\left(\frac{60}{750} \times 100\right) \% \\ &=8 \% \end{aligned}$
Question 7
Selling price -= Rs 3906; Loss = Rs 294
$\begin{aligned} \text { Loss }=&C \cdot p-s \cdot p\\ c \cdot p &=\text { Loss }+S \cdot p \\ &=294+3906 \\ &=4,200 . \end{aligned}$
Loss percent = $\left(\frac{\operatorname{loss} }{C.p} \times 100\right) \%$
$=\left(\frac{294}{4,200} \times 100\right) \%$
$=7 \%$
Question 8
C .P=Rs120, Loss percent =10%
Loss pescent $=\frac{\text { Loss }}{\text { c.p }} \times 100$
$\begin{aligned} \text { Loss } &=\frac{\text { Loss percent } c.p}{100} \\ &=\frac{10 \times 120}{100}=₹12\end{aligned}$
$\begin{aligned} \text { Loss }=& C \cdot p-s \cdot p \\ S \cdot p=&c\cdot p-\text { Loss }\\ &=120-12 \\ &=\ ₹108 \end{aligned}$
Question 9
cost price $=₹ 10,000 ;$ profit $=20 \%$
profit $\%=\frac{\text { Profit }}{C \cdot p} \times 100$
$20=\frac{\text { profit }}{10,000} \times 100$
profit $=\frac{20 \times 10,000}{10}$
profit $=20,00$
As profit = S.P - C.P
S.P =Profit + C.P
= 2000+ 10,000
S.P = Rs 12,000
∴ Selling price = Rs 12,000
Question 10
selling price =Rs 300; profit $=20 \%$
profit percentage $=\left(\frac{\text { profit }}{\text { c.p }} \times 100\right) \%$.
$=\left(\frac{S \cdot p-C\cdot p}{C \cdot p} \times 100\right) \%$
$=\left[\frac{s \cdot p}{c \cdot p}-1\right] \times 100$
$20=\left(\frac{300}{c \cdot p}-1\right) \times 100$
$\frac{300}{c \cdot p}-1=\frac{20}{100}$
$\cdot \frac{300}{c \cdot p}-1=\frac{1}{5}$
$\frac{300}{C \cdot p}=1+\frac{1}{5}=\frac{6}{5}$
$\frac{300}{C \cdot p}=\frac{6}{5}$
$C \cdot P=\frac{300 \times 5}{6}$
$c \cdot$ P=Rs 250
$\therefore$ cost price =Rs 250
Question 11
Selling price = Rs 320 ; Loss percent = 20 %
Loss percent = $\frac{\text { Loss }}{\text { c.p }} \times 100$
$=\frac{C p-s . p}{c \cdot p} \times 100$
$20=\left(1-\frac{320}{c \cdot p}\right) \times 100$
$1-\frac{320}{c \cdot p}=\frac{20}{100}$
$1-\frac{320}{c \cdot p}=\frac{1}{5}$
$\frac{320}{c \cdot p}=1 \frac{1}{5}$
$\frac{320}{6 \cdot p}=\frac{5-1}{5}$
$\frac{320}{c \cdot p}=\frac{4}{5}$
$c \cdot p=\frac{320 \times 5}{4}$
$c \cdot$ p=Rs 400
∴ Cost price = Rs 400
Question 12
selling price = Rs 522 ; profite 16%
profit $\%=\left(\frac{\text { profit }}{c \cdot p} \times 100\right)$
$=\frac{S \cdot p-c \cdot p}{C.p} \times 100$
$=\left(\frac{s \cdot p}{c \cdot p}-1\right) \times 100$
$16=\left(\frac{522}{c . p}-1\right) \times 100$
$\frac{522}{c.p}-1=\frac{16}{10}$
$\frac{522}{c \cdot p}-1=\frac{4}{25}$
$\frac{522}{c \cdot p}=1+\frac{4}{25}$
$\frac{522}{c \cdot p}=\frac{29}{25}$
$C \cdot p=\frac{522 \times 25}{29}$
$C \cdot$ p=Rs 750
$\therefore$ cost price =Rs 70
Question 13
selling price $=57360$; Loss $\%=8 \%$
$\begin{aligned} \text { Loss pescent } &=\left(\frac{\text { Loss }}{\text { c.p }} \times 100\right) \% \\ & \left.=\frac{C \cdot p-s \cdot p}{C \cdot p} \times 100\right) \end{aligned}$
$=\left(1-\frac{s \cdot p}{c \cdot p}\right) \times 100$
$8=\left(1-\frac{\partial 360}{c \cdot p}\right) \times 1$
$\frac{8}{100}=1-\frac{7360}{c. p}$
$\frac{2}{25}=1=\frac{7360}{c .p}$
$\frac{7360}{c p}=1-\frac{2}{25}$
$\frac{7360}{c \cdot p}=\frac{23}{25}$
$c.{p}=\frac{7360 \times 25}{23}$
$c \cdot$ p=Rs 8,000
cost price =Rs 8000
Question 14
Selling price= Rs 3168 ; Loss = $12 \%$
Loss percentage $=\frac{\text { Loss }}{C \cdot p} \times 100$
$=\left[1-\frac{S \cdot p}{C \cdot p}\right] \times 100$
$12=\left[1-\frac{3168}{c.p}\right] \times 100$
$1-\frac{3168}{6.8}=\frac{12}{100}$
$1-\frac{3168}{c\cdot p}=\frac{3}{25}$
$\frac{3168}{6 . p}=1-\frac{3}{25}$
$\frac{3168}{c. p}=\frac{22}{25}$
$c \cdot p=\frac{3168 \times 25}{23}$
C.p =Rs 3600
Given selling price = 3870
As S.P > C.P he gains
So gain = S.P - C.P = 3870-3600
= 270
Gain percentage = ($\frac{\text { Gain }}{\text { c.p }} \times 100$)%
$=\left(\frac{270}{3600} \times 100\right) \%$
=75 %
Question 15
selling price =Rs4550, Loss =9 %
Loss percent $=\left[1-\frac{S \cdot p}{C.p}\right] \times 100$
$9=\left[1-\frac{4550}{c \cdot p}\right] \times 100$
$1-\frac{4550}{c \cdot p}=\frac{9}{100}$
$\frac{4550}{c \cdot p}=1-\frac{9}{100}$
$\frac{4550}{c \cdot p}=\frac{91}{100}$
$c \cdot p=\frac{4550 \times 100}{91}$
$C \cdot$ p=Rs 5000
As given selling price = 4825
As C.P > S.P, so he lose
Loss = C.P - S.P
= 5000- 4825
Loss = Rs 175
Loss percent = ($\frac{\text { Loss }}{c. p} \times 100$)
$=\left(\frac{175}{5000} \times 100\right)$
$=3.5 \%$
EXERCISE:7.4
Question 1
Simple Interest $=\frac{\text { principal } \times \text { Rate } \times \text { Time }}{100}$
i.e $I=\frac{P \times R \times T}{100}$.
i) $\quad p=350 \quad ; \quad R=11 \% \quad T=2$ years
$I=\frac{350 \times 11 \times 2}{100}$
I=Rs 77
Total amount $=S \cdot I+P$
$=77+350$
=Rs 427
ii) $p=20,000 \quad T=4 \frac{1}{2}=\frac{9}{2}$ years $; R=8 \frac{1}{2}=\frac{17}{2} \%$
$\begin{aligned} I=& \frac{20,00 \times \frac{17}{2} \times \frac{9}{2}}{160} \\ &=\frac{20000 \times 17 \times 9}{4 \times 100} \\ &=₹ 7650 \end{aligned}$
∴ Amount = principal + I
=20,000+ 7,650
= 27,650
iii) $p=₹ 648 ; R=16 \frac{2}{3}=\frac{50}{3} ; T=8$ months = $\frac{8}{12}$ years
$I=\frac{648 \times \frac{50}{3} \times \frac{8}{12}}{100}$
$I=\frac{648 \times 50 \times 8}{36 \times 100}$
I=Rs 73
$\begin{aligned} \text { Amount } &=S \cdot 1+P \\ &=73+648 \\ &=₹ 721 \end{aligned}$
Question 2
i) $S \cdot I=200, \quad p=2,500, \quad R=4 \%$
$I=\frac{P \times R \times I}{100}$
Time, $T=\frac{100 \times \underline{1}}{P \times R} .$
$T=\frac{100 \times 200}{2,500 \times 4}$
$T=2$ years
ii) $S \cdot I=2730, \quad P=12,000, R=6 \frac{1}{2}=\frac{13}{2}$
$\begin{aligned} T=& \frac{100 \times I}{P \times R} \\=& \frac{100 \times 2730}{12,000 \times 13 / 2} \\ &=\frac{100 \times 2730 \times 2}{12000 \times 13} \end{aligned}$
$T=\frac{7}{2}$ years $=3 \frac{1}{2}$ years
Question 3
i) $P=1560, \quad I=585, \quad T=3$ yeass
$I=\frac{p \times R \times T}{100}$
Rate of interest R= $\frac{100 \times I}{P \times T}$
$R=\frac{100 \times 585}{1560 \times 3}=(1.25 \times 100) \%$
$R=\frac{25}{2} \%=12 \frac{1}{2} \%$
ii) $I=325, \quad p=1625, \quad T=2 \frac{1}{2}=\frac{5}{2}$ years
$\begin{aligned} R &=\frac{100 \times I}{P \times J} \\ &=\frac{100 \times 325}{1625 \times 5 / 2} \\ &=\frac{100 \times 325 \times 2}{1625 \times 5} \\ &=8 \% \end{aligned}$
Question 4
i) $R=16 \% ; T=2 \frac{1}{2}$ years $=\frac{5}{2}$ years, $I=3840$
$I=\frac{P R I}{100}$
$P=\frac{100 \times I}{R \times T}$
$P=\frac{100 \times 3840}{16 \times 5 / 2}$
$P=\frac{100 \times 3840 \times 2}{16 \times 5}$
P=Rs 9600
∴ Principal = Rs 9600
ii) $R=7 \frac{1}{2}=\frac{15}{2} \% \quad ; \quad T=2$ years 4 months $\quad I=2730$
$=\left(2+\frac{4}{12}\right)$ year
$=\left(2+\frac{1}{3}\right)$ years
$=\frac{7}{3}$ years
$\begin{aligned} P &=\frac{100 \times I}{R \times T} \\ &=\frac{100 \times 2730}{\frac{15}{2} \times \frac{7}{3}} \\ &=\frac{100 \times 2730 \times 6}{15 \times 7} \end{aligned}$
Principal p = Rs 15,600
Question 5
i) Amount = Rs 1320; Principal = Rs 1200
S.I = A-P = 1320 - 1200
S.I = 120
$I=\frac{P \times R \times I}{100}$
$R=\frac{100 \times I}{P \times T}$
$R=\frac{100 \times 120}{1200 \times 2}$
$R=5 \%$ per annum
ii) Amount=Rs 400; principal =Rs 300
$S: I=A-P=400-300$
I=Rs 100
$R=\frac{100 \times 100}{300 \times 2}$
$R=\frac{50}{3}=16 \frac{2}{3} \%$ pes annam.
Question 6
i) $A=1950, P=1250, R=16 \%$
$I=A-P=1950-1250= 700$
$I=\frac{P \times R \times T}{100}$
$T=\frac{100 \times I}{P \times R}$
$T=\frac{100 \times 700}{1250 \times 16}$
$\quad$ Time, $T=\frac{7}{2}$ years
ii) $A=8447.50, P=6540 ; R=12 \frac{1}{2}=\frac{25}{2} .$
$I=A-P=8447.5-6540$
$I=19075$
Time, $\begin{aligned} T &=\frac{100 \times 1907.5}{6540 \times 25 / 2} \\ T &=\frac{100 \times 19075 \times 2}{6540 \times 25} \end{aligned}$
Time, $T=\frac{7}{3}$ years
Question 7
$R=4 \% \quad A=16,240, \quad P=14,000$
$\begin{aligned} I=& A-P=16,240-14,000 \\ & I=2,240 . \\ \text { Time } &=\frac{100 \times I}{P \times R} \\ \text { Time } &=\frac{100 \times 2,240}{14,000 \times 4} \\ &=4 \text { years } \end{aligned}$
Question 8
$T=6$ years, Given Amount invested trebled
So A 3 $\times$ Principal
A = 3p
$\begin{aligned} I=& A-\rho=3 p-p \\ & I=2 p \\ I=& \frac{P \times R \times f}{100} \\ R &=\frac{100 \times 1}{p \times 1} \\ & R=\frac{100 \times 20}{P \times 6} \\ & R=\frac{100}{3}=33 \frac{1}{3} \% \text { pes annm } \end{aligned}$
Question 9
i) $A=4,500 ; R=20 \% T=5$ years
$I=A-P$
$I=4,500-P$
Also $I=\frac{p \times R \times {j}}{100}$
$4,500-P=\frac{P \times 20 \times 5}{100}$
$4,500-P=P$
$\begin{aligned} p+p=& 4,500 \\ 2 p=4,500 \\ \text { principal, } P=2250 \end{aligned}$
ii) $A=2420, R=4, \quad T=2 \frac{1}{2}$ yeass $=\frac{5}{2}$ years
$I=A-P$
$I=2420-P$
Also $I \cdot \frac{P \times R \times 1}{100}$
$2420-p=\frac{p \times 4 \times 5}{2 \times 100}$
$2420-R=\frac{1}{10}$
$P+\frac{p}{10}=2420$
$\frac{11P}{10}=2420$
$P=\frac{2420 \times 10}{11}$
$P=2200$
$\therefore$ principal, $p=2,200$
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