ML AGGARWAL CLASS 8 CHAPTER 7 Percentage Exercise 7.2

    Exercise 7.2

Question 1

Sol :

(i) C.P 400  S.P = 468

 $\begin{aligned} \text { S.P }>\text { c.p , profit } &=\text { s.p-C.p } \\ &=468-400 \\ &=68 \end{aligned}$

profit percentage = $=\left(\frac{ \text { profit }}{c \cdot p} \times 100\right) \%$

$=\left(\frac{68}{400} \times 100\right) \%$

=17

(ii) C.P = 13600  , S.P = 12104

As C.p $>$ S. P $\begin{aligned} \text { Loss } &=c.p-s \cdot p\\ &=13,600-12,10 y \\ &=1496 \end{aligned}$

loss percentage  

$\begin{aligned} &=\left(\frac{\text { Loss }}{c . p} \times 100\right) \% \\ &=\left(\frac{1496}{13600} \times 100\right) \% \\ &=11 \% \end{aligned}$ 

Question 2

Sol :

Given $S \cdot P=1636.25$, gain $=96.25$

As $Gain=S \cdot p-C p$

⇒ $\begin{aligned} C \cdot P=S \cdot p-G a i n &=1636.25-96.25 \\ &=1540 . \end{aligned}$

⇒ Gain percentage

 $\begin{aligned} &=\left(\frac{G a i n}{c \cdot p} \times 100\right) \% \\ &=\left(\frac{96 \cdot 25}{1540} \times 100\right) \% \\ &=6.25 \% \end{aligned}$

Question 3

Sol :

Given 

         S.P = 770  LOSS = 110

As loss = c.p - s.p 

c.p = loss + s.p 

= 110 + 700

⇒ 880

Loss percentage 

$\begin{aligned} &=\left(\frac{\text { Loss }}{c . p} \times 100\right) \% \\ &=\left(\frac{110}{880} \times 100\right) \% \\ &=12.5 \% \end{aligned}$

Question 4

Sol :

c.p of 1 dozen eggs $=9.60$

c.p of 25 dozen eggs $=(25 \times 9.6)=240$

Total no of eggs $=25 \times 12=300$ eggs

Out of 300 eggs, 30 eggs were broken

So the remaining no of eggs were 300 - 30 = 270 eggs 

Given  

S.P of each egg = Rs 1 

S. of 270 eggs $=270 \times 1=270$

As $S \cdot p>c. p$, he always gets profit on given

So the gain percentage = $\left(\frac{gain }{c \cdot p} \times 100\right) \%$

Gain = S.P - C.P 

⇒ 270 - 240 = 30 

Gain percentage = $\left(\frac{30}{240} \times 100\right) \%$

$=12.5 \%$

Question 5

Sol :

C.P of an article
$\begin{aligned} &=20,000+1400 \text { (repairs) } \\ &=21,400 \end{aligned}$

profit percentage =20 %

$\frac{\text { profit }}{\text { c.p }} \times 100=20$

Profit $x  \times100=20 \times 21,400$

$(SP-CP)=20 \times 214$

S.P-21,400=4280

$\begin{array}{l}S p=21,400+4280 \\ s p=25680\end{array}$

Selling price of an article = 25,680

Question 6

Sol :

C.P of bicycles includes

(i) 200 bicycles at 1200. per bicycle $=(200 \times 1200)=240000$

(ii) 301- per bicycle on transportation $=200 \times 30=6000$

(iii) 40001- on advertising =4000

Total cost price of bicycles =2,40,000+6000+4000

S.P of 200 bicycles $=200 \times 1350$

As SP>CP, there is always a gain

So Gain =SP-CP

$\begin{array}{l}=2,70,000-2,50,000 \\=20,000\end{array}$

$=\frac{Gain}{c . p} \times 100$

$=\frac{20,000}{2,50000} \times 100$

=8 %

Question 7

Sol :

Let S.P be ₹ x ,

then CP 90 % of x 

$=\frac{9}{10} x$

$\begin{aligned} \text { Profit } &=s \cdot p-c \cdot p \\ &=x-\frac{9 x}{10} \\ &=\frac{x}{10} \end{aligned}$

$\begin{aligned} \text { profit percentage }=&\left(\frac{\text { Profit }}{\text { c. } p} \times 100\right) \% \\ &=\left(\frac{(x / 10)}{(9 \times 10)} \times 100\right) \% \\ &=\frac{100}{9} \% \\ &=11.11 \% \end{aligned}$

Question 8

Sol :

(i) CP of 4 note boots $= ₹35$

then c.s of 1 note book $=\frac{35}{4}=8.75$ 

Sp of 5 note books =58

then $s \cdot p$ of 1 notebook $=\frac{58}{5}=11.6 \%$

As. SP>CP there is always a gain

Gain = SP-CP = 11.6 - 8.75

= 2.85

Gain percentage 

$\begin{aligned} &=\frac{G a i n}{C \cdot p} \times 100 \\ &=\frac{2.85}{8.25} \times 100 \\ &=32.57 \% \end{aligned}$

(ii) Number of notebooks to be sold = $\frac{\text { total profit }}{\text { profit on one notebooks }}$

$=\frac{171}{2.85}$

=60 

Question 9

Sol :

Cost price of 3 bananas = Rs 1 

The c .p of 1 banana = Rs $\frac{1}{3}=0.33$

S.p of 4 bananas = Rs 1

Then S.P of 1 banana = Rs $\frac{1}{4}=0.25$

As C.P>SP, These is always a loss.

$\begin{aligned} \text { Loss } &=C \cdot p-s \cdot p \\ &=\frac{1}{3}-\frac{1}{4} \end{aligned}$

$=\frac{1}{12}$

$\begin{aligned} \text { Loss percentage } &=\frac{\text { Loss }}{c . p} \times 100 \% \\ &=\frac{(1 / 12)}{(1 / 3)} \times 100 \% \\ &=\frac{100}{4} \% \\ &=25 \% \end{aligned}$

Question 10

Sol :

Given S.P of 5 pens = C.P of 7 pens

let cost price of one pen be x then 

C.P of  7 pens = Rs 7x

It is given 

S.P of 5 pens = c.p of 7 pens 

S.P of 5 pens = rs 7x 

S.P of one pen = $\frac{7 x}{5}$

As  SP>C.P there is a profit

$\begin{aligned} \text { profit } &=S\cdot p-c \cdot p \\ &=\frac{7 x}{5}-x=\frac{2 x}{5} \end{aligned}$

∴ $\begin{aligned} \text { Profit percentage } &=\frac{\text { profit }}{C \cdot p} \times 100 \% \\ &=\frac{(2 x / 5)}{x} \times 100 \% \\ &=\frac{200}{5} \% \\ &=40 \% \end{aligned}$

Question 11

Sol :

(i) CP=2360, profit =8 %

As. Profit percentage $=\frac{\text { profit }}{C. p} \times 100$

$\begin{aligned} \text { profit } \times 100 &=8 \times 2360 \\ \text { profit } &=\frac{8 \times 2360}{100} \\ S.P-C \cdot p &=188.8 \\ S \cdot p &=2360+188 \cdot 8 \\ S \cdot P &=2548.8 \end{aligned}$

(ii) CP=380 ; loss=7.5 %

Loss percentage $=\frac{\text { loss }}{\text { C.P }} \times 100$

Loss $=\frac{7.5 \times 380}{100}$

$\begin{aligned} c\cdot p-s .p &=28.5 \\ s \cdot p &=380-28.5 \\ s \cdot p &=351.5 \end{aligned}$

Question 12

Sol :

CP of dozen egg =18

then CP of 1 egg=$\frac{18}{12}=21.5$

⇒Profit =50 %

$\frac{SP-CP}{C. P} \times 100=50$

SP-CP=9

SP=18+9

SP=27

S.P of 1 egg  =$\frac{27}{12}=22.25$

Question 13

Sol :

Let the no of wrist watches are x 

cost of x wrist watches Rs 60,000

C.P one third of wrist watches will worth 20,000

(i) As we know $\frac{1}{3} \mathrm{rd}$ are sold at a 30% profit

$\begin{aligned} S \cdot p &=\left[1+\frac{P}{100}\right] \text { of } C. P \\ &=\left[1+\frac{30}{100}\right] \times 20,000 \\ &=\frac{130}{100} \times 20,000 \\ &=26,000 \end{aligned}$

(ii) $SP=\left[1+\frac{p}{100}\right]$ of CP $\left[\because\right.$ 

As $\frac{1}{3}$rd are sold at 20 % gain]

$=\left[1+\frac{20}{100}\right] \times 20,000$

$=\frac{120}{100} \times 20,000$

=24,000

(iii) $S \cdot P=\left(1-\frac{l}{100}\right)$ of c.p [Remaining are sold at a 5 % Less ]

$=\left[1-\frac{5}{100}\right] \times 20,000$

$=\frac{95}{100} \times 20,000$

=19,000

Total cost price = ₹ 60,000

$\begin{aligned} \text { Selling price } &=[26,000+24,000+19,000] \\ &=69000 \end{aligned}$

As SP>CP these is always a profit

$\begin{aligned}G a i n=S \cdot p-C \cdot p &=69,000-60,000 \\&=9,000\end{aligned}$

Gain percentage

$=\begin{aligned} &=\frac{G a i n}{c \cdot p} \times 100 \% \\ &=\frac{9,000}{69,000} \times 100 \% \\ &=15 \% \end{aligned}$

Question 14

Sol :

C.P of a Laptop = 40,000

C.P of a mobile phone =  24,000

Total CP of whole Transaction =40,000+24,000

=64,000

As shopkeeper made a profit of 8 % on laptop

$\text { So. } \begin{aligned}s \cdot p &=\left(1+\frac{p}{100}\right) \text { of } c \cdot p \\&=\left[1+\frac{8}{100}\right] \times 40,000 \\&=\frac{108}{100} \times 40,000 =43,200\end{aligned}$

Also, he made a loss of 12 % on mobile phone

$\begin{aligned}SP &=\left[1-\frac{l}{100}\right] \text { of } C \cdot P \\&=\left[1-\frac{12}{100}\right] \times 24,000 \\&=\frac{88}{100} \times 24,000 \\&=21,120\end{aligned}$

Total S.P on whole Transaction =43,200+21,120

=64,320 .

As, SP>CP there is always a gain

$\begin{aligned}\text { Gain }=S \cdot p-c \cdot p &=64,320-64,000 \\&=320 \\\text { Gain percentage } &=\frac{G a i n}{C i p} \times 100\end{aligned}$

=0.5 %

Question 15

Sol :

C.P of 40 chairs $=(40 \times 175)=7,000$

Desired gain on whole deal =10%

SP of all chairs $=\left[1+\frac{10}{100}\right] \times 7,000$

$=\frac{110}{100} \times 7,000$

=7,700

One-Fourth of all articles $=\frac{1}{4} \times 40=10$

C.P of 10 articles $=10 \times 175=1750$

As these articles are sold at a loss of 8 %

SP of these articles $=\left[1-\frac{8}{100}\right]$ of 1750

$=\frac{92}{100} \times 1750$

=1610

Selling price of remaining i .e 30 chairs = 7700- 1610 = 6090

∴ SP of each of the remaining chairs = $\frac{6090}{30}$

 =₹203

Question 16

Sol :

S.P of two electronic gadgets = Rs 44,000 (each)

for first gadget 

SP= rs 44,000  , profit = 10% , C.P = ?

$\begin{aligned} 44,000 &=\left(1+\frac{10}{100}\right) \text { of }(. P) \\ C \cdot P &=Rs\left(44,000 \times \frac{100}{110}\right)=Rs 40,000 \end{aligned}$

For second gadget:

$\begin{aligned} S \cdot p=44,000 &, \text { loss }=12 \%, C \cdot p=9 \\ \text { S. } \rho &=\left[1-\frac{1}{100}\right] \text { of } C \cdot P \\ 44,000 &=\left[1-\frac{12}{100}\right] \text { of } C \cdot P \\ C \cdot P &=\left\{\left[44,000 \times \frac{100}{88}\right]=\{50,000 .\right.\end{aligned}$

Then, Total cost price =40,000+50,000=90,000

Total selling $\rho_{i}(e=44,000+44,000=88,000$

Loss =CP-SP=90,000-88,000=2,000

Loss percentage

 $\begin{aligned} &=\frac{\text { Loss }}{C.{P}} \times 100 \\ &=\frac{2,000}{99,000} \times 10 \% \\ &=\frac{20}{9} \\ &=2.22 \% \end{aligned}$

Question 17

Sol :

Manufacturing price of a TV set =12,000

Shopkeeper Sold to a dealer at a profit of 20 %

Now s.p of de T.V $\operatorname{set}=\left[1+\frac{20}{100}\right]$ of CP

$\begin{aligned} S \cdot p &=\frac{120}{100} \times 12,000 \\ &=1.4,000 \end{aligned}$

Dealer sold to a customer at 12.5 % profit

Now Dealer's s.p will become cost price

So, New selling price to Customer

$\begin{array}{l}=\left[1+\frac{12.5}{100}\right] \text { of } C P \\ =\frac{112.5}{100} \times 14,000\end{array}$

= 16,200

So the customer pay 16200 for T .V SET 

Question 18

Sol :

(i) SP=450,  Loss=10 %

$\begin{aligned} \% \text { Loss } &=\frac{\text { Loss }}{c \cdot p} \times 100 \\ 10 &=\left[1-\frac{s \cdot p}{c \cdot p}\right] \times 100 \\ 1-\frac{s \cdot p}{c \cdot p} &=\frac{1}{10} \end{aligned}$

$\frac{S \cdot p}{C .P}=1-\frac{1}{10}=\frac{9}{10}$

$CP=\frac{450 \times 10}{9}$

CP=₹ 500

(ii) $\begin{aligned} S p=690 &, \text { profit }=15 \% \\ S \cdot p &=\left[1+\frac{p}{100}\right] \text { of }C\cdot p\\ 690 &=\left[1+\frac{15}{100}\right] \times C . p \\ C \cdot \rho &=\frac{690 \times 100}{115} \\ C \cdot &=Rs 600 \end{aligned}$

Question 19

Sol :

If S.P = 3920 , gain = 12 %

$S \cdot p=\left[1+\frac{p}{100}\right]$ of $c \cdot p$

$3920=\left[1+\frac{12}{100}\right] \times C . p$

$c \cdot p=\frac{3920 \times 100}{112}$

C.P = 3,500

Now S.P= 4375

As SP>$CP

Gain =SP-CP

=4,375-3,500

=875

Gain percentage

$\begin{aligned} &=\left[\frac{G a i n}{c \cdot p} \times 100\right] \% \\ &=\left[\frac{875}{3,500} \times 100\right] \% \\ &=25 \% \end{aligned}$

Question 20

Sol :

SP=1334 , Loss =8 %

$S \cdot p=\left[1-\frac{1}{100}\right]$ of $C \cdot p$

$1334=\left[1-\frac{8}{100}\right] \times C . p$

$\begin{aligned} C \cdot p &=\frac{1334 \times 100}{92} \\c\cdot p&= 1450 \end{aligned}$

Given profit $=12 \frac{1}{2} \%=12.5 \%$

Now $S \cdot p=\left[1+\frac{p}{100}\right] \times(c.p)$

$=\left[1+\frac{12.5}{100}\right] \times 1450$

$S \cdot p=\frac{112.5 \times 1450}{100}$

SP=21631.25

Question 21

Sol :

$\begin{aligned} S \cdot p=252 \cdot & \text { Gain }=5 \% \\ S \cdot P=&\left[1+\frac{P}{100}\right] \times C \cdot \rho \\ C \cdot P &=\frac{s.p \times 100}{100+P} \\ &=\frac{252 \times 100}{100+5} \\ & C \cdot p=\frac{25200}{105}=240 \end{aligned}$

SP=? if gain=35 %

$SP=\left[1+\frac{p}{100}\right]$ of CP

$=\left[1+\frac{35}{100}\right] \times 240$

$S \cdot 1=\frac{135 \times 240}{100}$

SP=2324

Question 22

Sol :

Let the selling price of a bag be ₹ x

profit = 12 % 

$x=\left(1+\frac{12}{100}\right) d f \cdot p$

$\begin{aligned} x=\frac{112}{100} & \text { of }(\cdot p\\ c \cdot p &=\frac{100 x}{112} \end{aligned}$

To make 18 % profit

$SP=\left[1+\frac{18}{100}\right] \text { of } CP$

$=\frac{118}{100} \times \frac{100 x}{112}=\frac{59 x}{56}$

According to given in formation, $\frac{59 x}{56}=x+39$

$\frac{59 x-x}{56}-39$

$\frac{3 x}{56}=3913$

$x=56 \times 13$

x=728=SP

$\begin{aligned} \text { Cost price of } b a g &=\frac{100 \times x}{112} \\ &=\frac{100 \times 728}{112} \\ \text { Cost price of bag } &=₹650 \end{aligned}$

Question 23

Sol :

Let the S.P of Sweater be x, loos =5 %

$\begin{array}{l}x=\left[1-\frac{5}{160}\right] \text { of } c \cdot p \\ \quad C \cdot p=\frac{100 x}{95}\end{array}$

To make 15 % profit

$\begin{aligned} \text { S. } p=\left[1+\frac{15}{100}\right] \text { of } C \cdot p &=\left[1+\frac{15}{100}\right] \times \frac{100 x}{95} \\ &=\frac{115}{100} \times \frac{100 x}{95}=\frac{23 x}{19} \end{aligned}$

According to given information, $\frac{23 x}{19}=x+260$

$\begin{array}{c}\frac{4 x}{19}=260 \\ x=65 \times 19 \\ x=1235\end{array}$

$\therefore$ Selling price of . Sweater =1,235

Question 24

Sol :

Let the selling price be "x" 

Loss =8 %

$\begin{array}{c}x=\left[1-\frac{8}{100}\right] \text { of } c \cdot p \\ c \cdot p=\frac{100 x}{92}\end{array}$

To make a profit of 12 % 

$\begin{aligned} S \cdot P=\left[1+\frac{12}{100}\right] \ of c\cdot p&=\left[\frac{112}{100} \times \frac{100 x}{92}\right] \\ &=\frac{28 x}{23} . \end{aligned}$

According to given information, $\frac{28 x}{23}=x+150$

$\frac{5 x}{23}=150^{30}$

Selling price, $x=23 \times 30=₹690$