Exercise 8G
Question 1
Find the profit or loss per cent.
(a) C.P. = Rs. 500, S.P. = Rs. 650
Sol :
Profit=(650-500)=150
∴Profit %$=\left(\frac{150}{500}\times 100\right)$=30%
(b) C.P. = Rs. 900, S.P = Rs. 828
Sol :
Loss=900-828=72
∴Loss %$=\left(\frac{72}{900}\times 100\right)$=8%
(c) C.P. = Rs. 325, overheads = Rs. 25, S.P = Rs. 490
Sol :
Total CP=325+25=350
∴Profit %$=\left(\frac{490-350}{350}\times 100\right)$%
$=\left(\frac{140}{350}\times 100\right)$=40%
Question 2
Find the S.P. of an article if its
(a) C.P. = Rs. 80, profit = 15%
Sol :
Profit$=80 \times \frac{15}{100}$=12
∴SP=80+12=92
(b) C.P = Rs. 950, loss = 8%
Sol :
Loss$=950\times \frac{8}{100}$=76%
SP=950-76=874
(c) C.P = Rs. 190.50, octroi = Rs. 20.50, transportation charges = Rs. 59, loss = 20%
Sol :
Total CP=190.50+20.50+59=270
∴SP$=\frac{100-20}{100}\times 270$
$=\frac{80}{100}\times 270$
=216
Question 3
Find the C.P. if
(a) S.P. = Rs. 2380, profit = 19%
Sol :
CP$=\left(\frac{100}{100+\text{gain %}}\times \text{SP}\right)$
$=\frac{100}{100+19}\times 2380$
$=\frac{100}{119}\times 2380$
=2000
(b) S.P. = Rs. 510, loss = 15%
Sol :
CP$=\left(\frac{100}{100+\text{gain %}}\times \text{SP}\right)$
$=\frac{100}{85} \times 510$
=600
Question 4
A person buys a book for Rs. 200 and sells it for Rs. 225. What will be his gain per cent?
Sol :
Gain%$=\left(\frac{225-200}{200}\times 100\right)$%
$=\frac{25}{200}\times 100$%
=12.5%
Question 5
A calculator is bought for Rs. 350 and sold at a gain of 15%. What is the selling price of calculator?
Sol :
∴S.P$=\frac{100+15}{100}\times 350$
$=\frac{115}{10}\times 35$
=402.50
Question 6
By selling a cellphone for Rs. 2400 a shopkeeper makes a profit of 25%. What would be his profit percentage if he sells it for Rs. 2040?
Sol :
C.P$=\frac{100}{100+25}\times 2400$
$=\frac{100}{125}\times 2400$
=1920
Profit %$=\left(\frac{2040-1920}{1920}\times 100\right)$%
$=\left(\frac{120}{1920}\times 100\right)$%
=6.25%
Question 7
The owner of a cell phone charges his customer 23% more than the cost price. Find the cost price, if a customer paid Rs. 7011 for his cellphone.
Sol :
C.P$=\frac{100}{100+23}\times 7011$
$=\frac{100}{123}\times 7011$
=5700
Cost price of the phone 5700
Question 8
By selling an article for Rs. 100, a man gains Rs. 15. Find his gain %.
Sol :
C.P=100-15=85
Gain %$=\left(\frac{15}{85}\times 100\right)$%
=17.65%
Question 9
A trader sells an article and loses 12 and 1/2%. Find the ratio of cost price of the selling price.
Sol :
Let, the CP of an article be 100
∴SP of an article $=\left(100-12\frac{1}{2}\right)$
=100-12.5=87.5
Ratio of CP and SP= 100 : 87.5
=8 : 7
Question 10
A person purchased 10 dozen pens at the rate of Rs. 40 per dozen. On checking, he found that 20 pens were not working. In order to earn 25% profit, at what price should he sell each pen?
Sol :
10 dozen pens =10×12=120
Rate of per pen $=\frac{40}{12}$
Out of 120 pen 20 pens not working 100 pens working
Price of 100 pens$=\frac{20}{6}\times 100$
=333.3
≃334
25% profit on 334$=\frac{25}{100}\times 334$
=83.5
≃84
25% Profit on 100 pens =(334+84)=418
25% profit on each pen$=\frac{418}{100}$
=4.18
≃5
Ans : He should sell each pen at 5 Rs
Question 11
When a plot is sold for Rs. 18,700, owner loses 15%. At what price must the plot be sold in order to gain 15%?
Sol :
CP of plot$=\frac{100}{100-15}\times 18700$
$=\frac{100}{85} \times 18700$
=22000
To gain 15% , SP of plot$=\frac{100+15}{100}\times 22000$
=115×220=25300
SP of the plot is 25300
Question 12
By selling a small plot for Rs. 80,000, I gain 25 per cent. What per cent will i lose if i sell it for Rs. 56,000?
Sol :
CP$=\frac{100}{100+25}\times 80000$
$=\frac{100}{125} \times 80000$
=64000
∴Lose percentage$=\left(\frac{64000-56000}{64000}\times 100\right)$%
$=\left(\frac{8000}{64000}\times 100\right)$%
=12.5 %
Question 13
A man purchased a car for Rs. 1,35,000 and spent Rs. 25,000 on repairs. At what price was the car sold, if he suffered 10% loss on it?
Sol :
Total CP=135000+25000
=160000
Loss=10%
∴Then profit$=160000 \times \frac{10}{100}$
=16000
∴Total SP=160000-16000=144000
Question 14
Sudhir earned a profit of 20% by selling 60 apples at the rateof Rs. 42.50 for 5 apples. Find the total cost at which the apples were bought.
Sol :
Rate of 60 apples$=4250 \times \frac{60}{5}$
=2510
∴CP of apples$=\left(\frac{100}{100+20}\times 510\right)$
$=\left(\frac{100}{120}\times 510\right)$
=425
Question 15
The cost price of 16 pens is equal to the selling price of 12 pens. Find the gain or loss percent?
Sol :
$\frac{SP}{CP}=\frac{16}{12}=\frac{4}{3}$
Loss %$=\frac{4-3}{3}\times 100=\frac{1}{3}\times 100=33\frac{1}{3}$
Ans : Loss$=33\frac{1}{3}$%
Question 16
If the selling price of 4 articles is equal to the cost price of 5 articles. Find the profit percent?
Sol :
5CP=4SP
$\frac{CP}{SP}=\frac{4}{5}$
∴Profit%$=\frac{5-4}{4}\times 100$
$=\frac{1}{4}\times 100$
=25
Ans : Profit =25%
Question 17
A fruit seller buys 700 oranges at the rate of Rs. 500 for 100 oranges and another variety of 500 oranges at the rate of Rs. 700 for 100 oranges and sells them at Rs. 84 per dozen. Find the profit per cent.
Sol :
CP of 700 oranges$=\left(\frac{500\times 700}{100}\right)$
=3500
CP of 500 oranges of another variety$=\left(\frac{700}{100}\times 500 \right)$
=3500
∴Total CP=3500+3500=7000
Total number of oranges purchased=700+500=1200
∴Total SP$=\left(\frac{84}{12}\times 1200\right)$
=8400
∴Profit%$=\left(\frac{8400-7000}{7000}\times 100\right)$%
$=\left(\frac{14000}{7000}\times 100\right)$%
=20%
Question 18
Some articles were bought at 6 for Rs. 5 and sold at 5 for Rs. 6. Find the gain per cent.
Sol :
Let, Number of articles bought =30
∴CP of 30 articles $=\left(\frac{5}{6}\times 30\right)$
=25
∴SP of 30 articles$=\left(\frac{6}{5}\times 30\right)$
=36
∴Gain%$=\left(\frac{36-25}{25}\times 100\right)$%
$=\left(\frac{11}{25} \times 100\right)$%=44%
Question 19
An article is sold at a gain of 15%. Had it been sold for Rs. 27 more, the profit would have been 20%. Find the cost price of the article.
Sol :
100 units CP
15% gain SP1=115
20% gain SP2=120
So, 5 unit =27
1 unit $=\frac{27}{5}$
∴100$=\frac{27}{5}\times 100$=540
CP of the article 540
Question 20
A dealer sold two types of goods for Rs. 10,000 each. On one of them, he lost 20% and on the other, he gained 20%. Find his gain or loss per cent on the entire transaction.
Sol :
Total SP=10000+10000=20000
Since, we know that
CP on loss$=SP \times \frac{100}{100-20}$
CP on profit$=SP\times \frac{100}{100+20}$
∴Total CP$=\left[10000\times \frac{100}{100-20}\right]+\left[10000\times \frac{100}{100+20}\right]$
$=\left(10000\times \frac{100}{80}\right)+\left(10000 \times \frac{100}{120}\right)$
$=50000\times \left(\frac{1}{4}+\frac{1}{6}\right)$
$=50000\times \frac{3+2}{12}=\frac{62500}{3}$
∴Loss$=\frac{62500}{3}-20000$
$=\frac{62500-60000}{3}=\frac{2500}{3}$
∴Loss %$=\left(\dfrac{\frac{250000}{3}}{\frac{62500}{3}} \times 100\right)$%
$=\left(\frac{2500}{62500}\times 100\right)$=4%
This is really very helpful
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