Exercise 8C
Question 1
Find the profit per cent, if an article purchased for Rs. 225 with overhead expenses of Rs. 15 is sold for Rs. 300.
Sol :
Cost Price(C.P)=225+15
=240
Selling Price(S.P)=300
∴Profit=SP-CP
=300-240=60
∴∴Profit%$=\frac{\text{profit }}{\text{CP}}\times 100$
$=\frac{60}{240}\times 100$
=25%
Question 2
By Selling an article for Rs. 960 a man incurs a loss of 4%. What is the cost price of the article?
Sol :
S.P=960
Loss=4%
CP$=\frac{\text{SP}}{100-4}\times 100$
$=\frac{960\times 100}{96}$
=1000
Question 3
If the cost price is 80% of the selling price, what is the profit per cent?
Sol :
Let, SP=100
CP$=100\times \frac{80}{100}$=80
∴Profit=SP-CP=100-80=20
∴Profit %$=\frac{\text{profit}}{\text{CP}}\times 100$
$=\frac{20}{80}\times 25$
=25%
Question 4
100 oranges are bought for Rs. 350 and sold at the rate of Rs. 48 per dozen. What is the percentage of profit or loss?
Sol :
100 orange$=\frac{25}{3}$dozen [∴1dozen=12 oranges]
$\frac{25}{3}$ dozen oranges Cost Price=350
1 dozen oranges Cost Price$=350\times \frac{3}{25}$=42
1 dozen oranges Selling Price =48
∴Profit=48-42=6
∴Profit %$=\frac{6}{42}\times 100$
$=14\frac{2}{7}$%
Question 5
The cost price of 25 articles is equal to the selling price of 20 articles. Find the profit per cent.
Sol :
Let, 25 articles Cost Price=100
Cost Price of 1 article$=\frac{100}{25}$=4
ATQ,
25 articles CP=20 articles SP=100
∴20 articles SP=100
∴1 articles SP$=\frac{100}{20}$=5
∴Profit=SP-CP=5-4=1
∴Profit%$=\frac{1}{4}\times 100=25/%$
Question 6
If I purchased 11 books for Rs. 1000 and sold 10 books for Rs. 1100, then find the percentage of profit.
Sol :
11 books CP=1000
1 book CP$=\frac{1000}{1}$
10 book SP=1100
1 book SP$=\frac{1100}{10}$=110
∴Profit$=110-\frac{1000}{1}$
$=\frac{1210-1000}{11}=\frac{210}{11}$
∴Profit%$=\dfrac{\frac{210}{11}}{\frac{100}{11}}\times 100$
$=\frac{210}{11}\times 100\times \frac{11}{1000}$
=21%
Question 7
An article is sold at a loss of 20%. There is a yield of Rs. 60 more if the article is sold at a profit of 20%. Find the cost price of the article.
Sol :
Let , CP of article=100
SP of article$=\frac{100-20}{100}\times 100$
=80
On being sold SP at gain of 20%$=\frac{120}{100}\times 100$=120
∴Difference of two SP=120-80=40
∵When CP is 100 then SP=40
∴When SP=60
The CP$=\frac{100\times 60}{40}=150$
Question 8
A person sells a table at a profit of 10%. If he had bought it at 5% less cost and sold for Rs. 80 more, he would have gained 20%. Find the cost price of the table.
Sol :
Let , CP of table=100
SP of table $=\frac{100\times 110}{100}$=100
He bought it 5% less
again CP2$=\frac{100\times 95}{100}$
Sold now at 80 more and gained 20%
SP2$=\frac{95\times 20}{100}+95$=114
Difference of SP1 and SP2=114-110=4
ATQ,
∴4x=80
1x$=\frac{80}{4}=20$
∴100x=20×100=2000
∴CP of table=2000
Question 9
A second hand car and a jeep were sold for Rs. 1,20,000 each. The car was sold at a loss of 20% while the jeep at a gain of 20%. What was the overall gain or loss?
Sol :
Cars SP=120000
Jeeps SP=120000
Loss for car=20%
Cars CP$=\frac{120000}{(100-20)}\times 100$
$=\frac{120000}{80}\times 100$
=150000
Gain for jeep=20%
∴Jeep's CP$=\frac{120000}{100+20}\times 100$
$=\frac{1000\times 120000}{120}\times 100$
=100000
∴Total CP=Car CP+Jeep CP=150000+100000
=250000
Total SP=SP+SP=120000+120000
=240000
∴Overall Loss=CP-SP=250000-240000
=10000
Question 10
The ratio of the cost price and selling price of an article is 20:21. Find the gain percent.
Sol :
CP : SP=20 : 21
Let, common factor=120
∴CP=20×1=20
SP=21×1=21
∴Gain=21-20=1
∴Gain %$=\frac{100\times 1}{20}=5 /%$
Question 11
A man buys a certain number of oranges at 20 for Rs. 60 and an equal number at 30 for Rs. 60. He mixes them and sells them at 25 for Rs. 60. What is his gain or loss percent?
Sol :
L.C. of number of oranges =300
CP of=20×15=300
=30×10=300
SP=25×12=300
∴Total CP=(900+600)=1500
SP=300+300 oranges
=720+720=1440
∴Loss=1500-1440=60
∴Loss%$=\frac{60}{1500}\times 100$
=4%
Question 12
If an article is sold for Rs. 105, there is a loss of 9%. At what price should the article be sold so that there is a gain of 30%?
Sol :
SP of article=105
Loss of articles=9%
CP of articles$=\frac{105\times 100}{91}$
Again gain of article=30%
∴SP of article$=\dfrac{130\left(\times \frac{105\times 100}{91}\right)}{100}$
$=130\times \frac{105\times 100}{91}\times \frac{1}{100}$
=150
Question 13
By selling 60 articles a vendor makes a profit equal to the selling price of 15 articles. Find his gain percentage.
Sol :
Let, SP of 1 article=x
SP of 60 articles=60x
SP of 15 articles=15x
∴We know that
Gain=SP-CP
ATQ,
SP-Gain=CP
60x-15x=CP
45x=CP
CP=45x
Now , Gain$=\frac{100\times 15x}{45x}$
$=33\frac{1}{3}$%
Question 14
The total cost price of two watches is Rs. 840. One is sold at a profit of 16% and the other at a loss of 12%. There is no loss or gain in the whole transaction. What is the cost price of the watch on which the shopkeeper gain?
Sol :
Total CP=840
Let , CP of 1st watch=x
∴CP of 2nd watch=(840-x)
For 1st watch➝
CP1=x
Profit=16%
∴SP1$=\frac{x\times 16}{100}=\frac{116x}{100}$
For 2nd watch➝
CP2=(840-x)
Loss=12%
∴SP2$=\frac{(840-x)\times 88}{100}=\frac{73920-88x}{100}$
ATQ,
$\frac{116x}{100}-x=(840-x)-\frac{(73920-88x)}{100}$
$\frac{116x-100x}{100}=\frac{840000-100x-73920+88x}{100}$
16x+100x-88x=840000-73920
28x=10080
x=360
Question 15
A shopkeeper gains 20% while buying the goods and 30% while selling them. Find his total gain percent.
Sol :
Let , a=20
b=30
We know that
Total gain%$=a+b+\frac{ab}{100}$
$=20+30+\frac{20\times 30}{100}$
=50+6=56%
Question 16
A dealer makes a profit of 20% even after giving a 10% discount on the advertised price of a scooter. What was the advertised price if he makes a profit of Rs. 7500 on the sale of the scooter?
Sol :
20% of profit=7500
∴100% of profit$=\frac{7500\times 100}{20}=37500$
Profit=7500
∴SP=37500+7500=45000
Let, advertise price be x
ATQ,
$x\times \frac{90}{100}=45000$
$x=\frac{45000\times 100}{90}$
x=50000
Question 17
A shopkeeper bought two TV sets at Rs. 10,000 each. He sold one at a profit of 10% and the other at a loss of 10%. Find whether he made an overall profit or loss.
Sol :
CP of each TV=10000
For 1st TV
CP1=10000
Profit=10%
∴SP1$=\frac{10000\times 110}{100}=11000$
For Second TV
CP2=10000
Loss=10%
∴SP2$=\frac{10000\times 90}{100}=9000$
∴Total SP=11000+9000=20000
∴Total CP=10000+10000=20000
∴There is neither profit nor loss
Question 18
A shopkeeper was selling his items at 25% discount. During the off season, he offered 30% discount over and above the existing discount. If Pragya bought a skirt was marked Rs. 1200, then how much did she pay for it?
Sol :
The marked price=1200
∴1st selling discount=25%
∴1st selling price$=\frac{1200\times 75}{100}$=900
Again 30% discount above & over the existing discount
∴2nd selling price$=\frac{900\times 70}{100}$=630
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