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 %
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