4 Mark Question - Maths STD 8 Questions - Vidyadip

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Question 14 Marks

Hema bought two pairs of jeans for Rs. 1450 each. She sold one of them at a gain of 8% and the other at a loss of 4%. Find her gain or loss percent in the whole transaction.

Answer

CP of first jeans = Rs. 1,450
Profit = 8% of CP $=\frac{8}{100}\times1450=\times1450=\text{Rs. }116$
SP of first jeans = Rs. 1,450 + Rs. 116 = Rs. 1,566
CP of second jeans = Rs. 1,450
Loss = 4% of CP $=\frac{4}{100}\times1450=\text{Rs. }58$
SP of second jeans = Rs. 1450 - Rs. 58 = Rs. 1,392
Total CP of two jeans = CP of first jeans + CP of second jeans
= Rs. 1,450 + Rs. 1,450 = Rs. 2,900
Total SP of two jeans = SP of first jeans + SP of second jeans
= Rs. 1,566 + Rs. 1,392 = Rs. 2,958
Here, Total SP of two jeans > Total CP of two jeans
Gain = Total SP of two jeans - Total CP of two jeans
= Rs. 2,958 - Rs. 2,900 = Rs. 58
$\therefore$ Gain % $=\frac{\text{gain}}{\text{total CP of two jeans}}\times100\%=\frac{58}{2900}\times100=2\%$

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Question 24 Marks

A radio is sold for Rs. 3120 at a loss of 4%. What will be the gain or loss percent if it is sold for Rs. 3445?

Answer

Let the original price be x
SP = Rs. 3120
Now, SP = CP - loss
$\Rightarrow3120=\text{x}-\frac{4}{100}$
$\Rightarrow3120=\text{x}-\frac{\text{x}}{100}$
$\Rightarrow3120=\frac{\text{24x}}{100}$
$\Rightarrow\frac{3120\times25}{100}=\text{x}$
$\Rightarrow\text{x}=3250$
So, the cost price is Rs. 3250
If it is sold for Rs 3445, then its a gain because SP > CP.
Now, gain = SP - CP
= Rs. (3445 - 3250)
= Rs. 195
$\therefore$ Gain percentage $=\Big(\frac{\text{gain}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{195}{3250}\times100\Big)\%=6\%$
Hence, gain percent = 6%

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Question 34 Marks

A jeweller allows a discount of 16% to his customers and still gains 20%. Find the marked price of a ring which costs the jeweller Rs. 1190.

Answer

Cost price of the refrigerator = Rs. 1190
Gain percentage = 20%.
$\therefore$ Selling price $=\Big\{\frac{(100+\text{gain}\%)}{100}\times\text{CP}\Big\}$
$=\Big\{\frac{100+20}{100}\times1190\Big\}$
$=\frac{120}{100}\times1190\ \text{Rs. }1428$
Let the marked price be Rs. x
Discount = 16% of Rs. x
$=\frac{16\text{x}}{100}$
S.P = MP - Discount
$\Rightarrow1428=\text{x}-\frac{16\text{x}}{100}$
$\Rightarrow1428=\frac{100\text{x}-16\text{x}}{100}$
$\Rightarrow142800=84\text{x}$
$\Rightarrow\text{x}=\frac{142800}{84}=\text{x}$
$\Rightarrow\text{x}=1700$
Therefore, the marked price of the ring is Rs. 1700

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Question 44 Marks

A dealer gets Rs. 56 less if instead of selling a chair at a gain of 15%, it is sold at a gain of 8%. Find the cost price of the chair.

Answer

Let Rs. x be the CP
$Gain_1$ percentage $=\Big(\frac{\text{gain}_1}{\text{CP}}\times100\Big)\%$
$\Rightarrow15=\frac{\text{gain}_1}{\text{x}}\times100$
$\Rightarrow\text{Gain}_1=\text{Rs. }\frac{15\text{x}}{100}$
Again, $gain_2$ percentage $=\Big(\frac{\text{gain}_1}{\text{CP}}\times100\Big)\%$
$\Rightarrow8=\frac{\text{gain}_2}{\text{x}}\times100$
$\Rightarrow\text{Gain}_2=\text{Rs. }\frac{8\text{x}}{100}$
According to the question, we have:
Gain $_1-$ gain $_2=56$
$\Rightarrow\frac{15\text{x}}{100}-\frac{8\text{x}}{100}=56$
$\Rightarrow\frac{7\text{x}}{100}=56$
$\Rightarrow7\text{x}=5600$
$\Rightarrow\text{x}=800$
Hence, the CP of the chair is Rs 800

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Question 54 Marks

Oranges are bought at 6 for Rs. 20 and sold at 4 for Rs. 18. Find the gain or loss percent.

Answer

CM of 6 and 4 = 12
Let the number of oranges bought be 12
CP of 6 oranges = Rs. 20
So, CP of 1 orange $=\frac{20}{6}=\text{Rs. }\frac{10}{3}$
CP of 12 orange $=12\times\frac{10}{3}=\text{Rs. }40$
SP of 4 oranges $=\text{Rs. }18$
SP of 1 orange $=\frac{18}{4}=\text{Rs. }\frac{9}{2}$
SP of 12 oranges $=12\times\frac{9}{2}=\text{Rs. }54$
Here, SP of 12 oranges > CP of 12 oranges
Profit = SP - CP = Rs. 54 - Rs. 40 = Rs. 14
$\therefore$ Profit % $=\frac{\text{profit}}{\text{CP}}\times100\%=\frac{14}{40}\times100\%=35\%$

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Question 64 Marks

Wasim bought two cricket bats for Rs. 840 and Rs. 360 respectively. He sells the first bat at a gain of 15% and the second one at a loss of 5%. Find his gain or loss percent in the whole transaction.

Answer

CP of the first bat = Rs. 840
Profit% on the first bat = 15%
$\therefore$ Profit = 15% of $\text{Rs. }840=\frac{15}{100}\times840=\text{Rs. }126$
SP of the first bat = Rs. 840 + Rs. 126 = Rs. 966
CP of the second bat = Rs. 360
Loss = 5% of $=\text{Rs. }360=\frac{5}{100}\times360=\text{Rs.}18$
SP of the second bat = Rs. 360 - Rs. 18 = Rs. 342
Total CP of two bats = CP of first bat + CP of second bat
= Rs. 840 + Rs. 360 = Rs. 1,200
Total SP of two bats = SP of first bat + SP of second bat
= Rs. 966 + Rs. 342 = Rs. 1,308
Here, Total SP of two bats > Total CP of two bats
Gain = Total SP of two bats - Total CP of two bats
= Rs. 1,308 - Rs. 1,200 = Rs. 108
$\therefore$ Gain% in the whole transaction
$=\frac{\text{gain}}{\text{total CP of two bats}}\times100\%=\frac{108}{1200}\times100=9\%$

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Question 74 Marks

A dealer purchased a fan for Rs. 1080. After allowing a discount of 25% on its marked price, he gains 25%. Find the marked price of the fan.

Answer

Cost price of the fan = Rs. 1080Gain percentage = 25%
$\therefore$ Selling price $=\Big\{\frac{(100+\text{gain}\%)}{100}\times\text{CP}\Big\}$
$=\Big\{\frac{100+25}{100}\times1080\Big\}$
$=\frac{125}{100}\times1080\ \text{Rs. }1350$
Let the marked price be Rs. x
Discount = 25% of Rs. x
$=\frac{25\text{x}}{100}$
SP = MP - discount
$\Rightarrow1350=\text{X}-\frac{25\text{X}}{100}$
$\Rightarrow1350=\frac{100\text{x}-25\text{x}}{100}$
$\Rightarrow1350=75\text{x}$
$\Rightarrow\text{x}=\frac{13500}{75}$
$\Rightarrow\text{x}=1800$
Therefore, the marked price of the fan is Rs. 1800

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Question 84 Marks

How much percent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 10% on the marked price, he gains 8%?

Answer

Let Rs. 100 be the cost price.
Gain required = 8%
Therefore, the selling price = Rs. 108
Let Rs. x be the marked price
Then, discount = 10% of Rs. x
$=\frac{10}{100}\times\text{x}=\frac{\text{x}}{10}$
Selling price = MP - Discount
$\Rightarrow117=\text{x}-\frac{\text{x}}{10}$
$\Rightarrow117=\frac{9\text{x}}{10}$
$\Rightarrow9\text{x}=1080$
$\Rightarrow\text{x}=\frac{1080}{9}$
$\Rightarrow\text{x}=120$
$\therefore$ Marked price = Rs. 120
Hence, the marked price is 20% above the cost price.

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Question 94 Marks

By selling a bouquet for Rs. 322, a florist gains 15%. At what price should he sell it to gain 25%?

Answer

SP of the bouquet = Rs. 322
Gain percentage = 15%
CP of the bouquet $=\Big(\frac{100}{100+\text{gain}\%}\Big)\times\text{SP}$
$=\text{Rs. }\Big(\frac{100}{100+150}\Big)\times322$
$=\text{Rs. }\frac{100}{115}\times322$
$=\text{Rs. }280$
Now, CP = Rs. 128 and desired gain percentage = 25%
$\therefore$ Desired SP $=\Big(\frac{100}{100+\text{gain}\%}\Big)\times\text{CP}$
$=\text{Rs. }\frac{125}{100}\times280$
$=\text{Rs. }350$
Hence, the selling price to obtain the desired gain must be Rs. 350.

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Question 104 Marks

If the selling price of 16 water bottles is equal to the cost price of 17 water bottles, find the gain percent earned by the dealer.

Answer

Let Rs. x be the SP of each bottle and Rs. y be the CP of each bottle. SP of 16 bottles = CP of 17 bottles.
⇒ 16x = 17y
$\Rightarrow\frac{\text{x}}{\text{y}}=\frac{17}{16}$
Gain per bottle = SP - CP
= Rs. x - y
$\therefore$ Gain percentage $=\Big(\frac{\text{gain}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{\text{x}-\text{y}}{\text{y}}\times100\Big)\%$
$=\Big\{\big(\frac{\text{x}}{\text{y}}-1\big)\times100\Big\}\%$
$=\Big\{\big(\frac{17}{16}-1\big)\times100\Big\}\%$
$=\Big(\frac{1}{16}\times100\Big)\%$
$=6\frac{1}{4}\%$

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Question 114 Marks

After allowing a discount of 10% on the marked price, a trader still makes a gain of 17%. By what percent is the marked price above the cost price?

Answer

Let Rs. 100 be the cost price.
Gain required = 17%
$\therefore$ Selling price = Rs. 117
Let the marked price be Rs. x
Then, discount = 10% of Rs. x
$=\frac{10}{100}\times\text{x}=\frac{\text{x}}{10}$
Selling price = MP - Discount
$\Rightarrow117=\text{x}-\frac{\text{x}}{10}$
$\Rightarrow117=\frac{9\text{x}}{10}$
$\Rightarrow9\text{x}=1170$
$\Rightarrow\text{x}=\frac{1170}{9}$
$\Rightarrow\text{x}=130$
$\therefore$ Marked price = Rs. 130
Hence, the marked price is 30% above the cost price.

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Question 124 Marks

A vendor purchased bananas at Rs. 40 per dozen and sold them at 10 for Rs. 36. Find his gain or loss percent.

Answer

LCM of 12 and 10 = 60
Let the number of banana bought be 60.
CP of 12 banana = Rs. 40
$\therefore$ CP of 1 banana $=\frac{40}{12}=\text{Rs. }\frac{10}{3}$
⇒ CP of 60 bananas $=60\times\frac{10}{3}=\text{Rs. }200$
SP of 10 bananas $=\text{Rs. }36$
$\therefore$ SP of 10 bananas $=\frac{36}{10}=\text{Rs. }\frac{18}{5}$
⇒ SP of 60 bananas $=60\times\frac{18}{5}=\text{Rs. }216$
Here, SP of 60 bananas > CP of 60 bananas.
Profit = SP - CP = Rs. 216 - Rs. 200 = Rs. 16
$\therefore$ Profit % $=\frac{\text{profit}}{\text{CP}}\times100\%=\frac{14}{40}\times100\%=8\%$

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Question 134 Marks

Coffee costing Rs. 250/kg was mixed with chicory costing Rs. 75/kg in the ratio 5 : 2 for a certain blend. If the mixture was sold at Rs. 230/kg, find the gain or loss percent.

Answer

Let 5kg of coffee be mixed with 2kg of chicory. CP of the mixture = Rs. (250 × 5 + 75 × 2) = Rs. (1250 + 150) = Rs. 1400 SP of the mixture = Rs. (7 × 230) = Rs. 1610 Since SP > CP, there is a gain. Now, gain = Rs. (1610 - 1400) = Rs. 210 Gain precentage $=\Big(\frac{\text{gain}}{\text{total CP}}\times100\Big)\%$ $=\Big(\frac{210}{1400}\times100\Big)\%$$=15\%$

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Question 144 Marks

By selling 130 cassettes, a man gains an amount equal to the selling price of 5 cassettes. Find the gain percent.

Answer

It is given that,
Gain = SP of 5 cassettes ...(1)
Gain = SP of 130 cassettes - CP of 130 cassettes
⇒ SP of 5 cassettes = SP of 130 cassettes - CP of 130 cassettes [From(1)]
⇒ CP of 130 cassettes = SP of 125 cassettes ...(2)
Let the CP of 1 cassette be Rs. x
$\therefore$ CP of 125 cassettes = Rs. 125x
CP of 130 cassettes = Rs. 130x
SP of 125 cassettes = CP of 130 cassettes [From (2)]
⇒ SP of 125 cassettes = Rs. 130x
Now, gain % $=\frac{\text{SP}-\text{CP}}{\text{CP}}\times100\%=\frac{(130\text{x}-125\text{x})}{125\text{x}}\times100\%$
$=\frac{5\text{x}}{125\text{x}}\times100\%=4\%$
Thus, the gain percent is 4%

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Question 154 Marks

A dealer bought a refrigerator for Rs. 11515. After allowing a discount of 16% on its marked price, he gains 20%. Find the marked price of the refrigerator.

Answer

Cost price of the refrigerator = Rs. 11515
Gain percentage = 20%.
$\therefore$ Selling price $=\Big\{\frac{(100+\text{gain}\%)}{100}\times\text{CP}\Big\}$
$=\Big\{\frac{100+20}{100}\times11515\Big\}$
$=\frac{120}{100}\times11515=\text{Rs. }13818$
Let the marked price be Rs. x
Discount = 16% of Rs. x
$=\frac{16\text{x}}{100}$
S.P = MP - Discount
$\Rightarrow13818=\text{x}-\frac{16\text{x}}{100}$
$\Rightarrow13818=\frac{100\text{x}-16\text{x}}{100}$
$\Rightarrow1381800=84\text{x}$
$\Rightarrow\text{x}=\frac{1381800}{84}$
$\Rightarrow\text{x}=16450$
Therefore, the marked price of the refrigerator is Rs. 16450

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Question 164 Marks

A man purchased some eggs at 3 for Rs. 16 and sold them at 5 for Rs. 36. Thus, he gained Rs. 168 in all. How many eggs did he purchase?

Answer

Let the number of eggs purchased be x
CP of 3 eggs = Rs. 16
$\therefore$ CP of 1 egg $=\text{Rs. }\frac{16}{3}$
⇒ CP of x eggs $=\text{Rs. }\frac{16}{3}\text{x}$
SP of 5 eggs $=\text{Rs. }36$
$\therefore$ SP of 1 egg $=\text{Rs. }\frac{36}{5}$
⇒ SP of x eggs $=\text{Rs. }\frac{36}{5}\text{x}$
Gain = SP - CP = Rs. 168
$\therefore\frac{36}{5}\text{x}-\frac{16}{3}\text{x}=168$
$\Rightarrow\frac{28}{15}\text{x}=168$
$\Rightarrow\text{x}=\frac{168\times15}{28}$
$\Rightarrow\text{x}=90$
Hence, the man purchased 90 eggs.

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Question 174 Marks

A dealer marks his goods at 35% above the cost price and allows a discount of 20% on the marked price. Find the gain or loss percent.

Answer

Let Rs. 100 be the CP
Then, marked price = Rs. 135
Discount = 20% of MP
$=\frac{20}{100}\times135=27$
Selling price = marked price - discount
= 135 - 27
= Rs. 108
Now, gain = SP - CP
= 108 - 100
= Rs. 8
$\therefore$ Gain percentage $=\frac{\text{gain}}{\text{CP}}\times100$
$=\frac{8}{100}\times100=8\%$

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Question 184 Marks

The marked price of a TV is Rs. 18500. A dealer allows two successive discounts of 20% and 5%. For how much is the TV available?

Answer

Marked price of the TV = Rs. 18500First discount = 20%
Now, 20% of 18500
$=\frac{20}{100}\times18500=\text{ Rs. }3700$
Price after the first discount = Rs. (18500 - 3700)= Rs. 14800
Second discount = 5% of 14800
$=\frac{5}{100}\times14800=740$
Price after the second discount = (14800 - 740) = Rs. 14060
The TV is available for Rs. 14060

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Question 194 Marks

A cellphone was marked at 40% above the cost price and a discount of 30% was given on its marked price. Find the gain or loss percent made by the shopkeeper.

Answer

Let Rs. 100 be the CP
Then, marked price = Rs. 140
Discount = 30% of MP
$=\frac{30}{100}\times140=42$
Selling Price = marked price - discount
= 140 - 42 = Rs. 98
Now, loss = CP - SP
= 100 - 98 = Rs. 2
$\therefore$ Loss percentage $=\frac{\text{loss}\times100}{\text{CP}}$
$=\frac{2\times100}{100}=2\%$
Therefore, the shopkeeper had a loss of 2%.

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Question 204 Marks

A dealer gets Rs. 940 more if instead of selling a table at a loss of 10%, it is sold at a gain of 10%. Find the cost price of the table.

Answer

Let the cost price be Rs. x.
Loss = 10% of $\text{Rs. }\text{x}=\frac{10}{100}\text{x}=\text{Rs. }\frac{\text{x}}{10}$
SP in case of loss = CP - Loss $=\text{x}-\frac{\text{x}}{10}=\text{Rs. }\frac{9\text{x}}{10}$
Gain = 10% of $\text{Rs. }\text{x}=\frac{10}{100}\text{x}=\text{Rs.}\frac{\text{x}}{10}$
SP in case of profit = CP + Profit $=\text{x}+\frac{\text{x}}{10}=\text{Rs. }\frac{11\text{x}}{10}$
It is given that dealer gets Rs. 940 more if sold at a profit of 10% instead of loss of 10%.
$\therefore$ SP in case of profit - SP in case of loss = Rs. 940
$\Rightarrow\frac{11\text{x}}{10}-\frac{9\text{x}}{10}=940$
$\Rightarrow\frac{2\text{x}}{10}=940$
$\Rightarrow\text{x}=4700$
Hence, the cost price of the table is Rs. 4,700

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Question 214 Marks

Sonu buys 40kg of wheat at Rs. 12.50/kg and 30kg of wheat at Rs. 14/kg. At what rate /kg should he sell the mixture to gain 5% on the whole?

Answer

40kg of wheat is bought for Rs. 12.50/kg
$\therefore$ CP of 40kg of wheat = 40 × 12.50 = Rs. 500
30kg of wheat is bought for Rs. 14/kg
$\therefore$ CP of 30kg of wheat = 30 × 14 = Rs. 420
Total CP = Rs. 500 + Rs. 420 = Rs. 920
Profit = 5% of CP $\text{Rs.}920=\frac{5}{100}\times920=46$
Let the SP be Rs. x
Profit = SP - CP
⇒ x - 920 = 46
⇒ x = Rs. 966
SP of 70kg wheat = Rs. 966
$\therefore$ SP of 1kg wheat $=\frac{966}{70}=13.80$
Thus, the selling price of the mixture is Rs. 13.80/kg.

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Question 224 Marks

Manjit bought an iron safe for Rs. 12160 and paid Rs. 340 for its transportation. Then, he sold it for Rs. 12875. Find his gain percent.

Answer

CP of the iron safe = Rs. 12,160
Money spent on transportation = Rs. 340
Total CP = Rs. 12,160 + Rs. 340 = Rs. 12,500
SP of the iron safe = Rs. 12,875
Profit = SP - CP = Rs. 12,875 - Rs. 12,500 = Rs. 375
$\therefore$ Profit % $=\frac{\text{Profit}}{\text{CP}}\times100\%=\frac{375}{12500}\times100\%=3\%$

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Question 234 Marks

A man bought apples at 10 for Rs. 75 and sold them at Rs. 75 per dozen. Find his loss percent.

Answer

LCM of 10 and 12 = 60
Let the number of apples bought be 60
CP of 10 oranges $=\text{Rs. }75$
$\therefore$ CP of 1 orange $=\text{Rs. }\frac{75}{10}$
⇒ CP of 60 orange $=60\times\frac{75}{10}=\text{Rs. }450$
SP of 12 oranges $=\text{Rs. }75$
$\therefore$ SP of 1 orange $=\text{Rs. }\frac{75}{12}$
⇒ SP of 60 oranges $=60\times\frac{75}{12}=\text{Rs. }375$
Here, CP of 60 oranges > SP of 60 oranges.
Loss = CP - SP = Rs. 450 - Rs. 375 = Rs. 75
$\therefore$ Loss % $=\frac{\text{loss}}{\text{CP}}\times100\%=\frac{75}{450}\times100\%=16\frac{2}{3}\%$

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Question 244 Marks

By selling an umbrella for Rs. 336, a shopkeeper loses 4%. At what price must he sell it to gain 4%

Answer

Let the CP of the umbrella be Rs. x
SP of the umbrella = Rs. 336
Loss = 4% of Rs. x $=\text{Rs. }\frac{4}{100}\text{x}$
CP - Loss = SP
$\Rightarrow\text{x}-\frac{\text{x}}{100}\text{x}=336$
$\Rightarrow\frac{96}{100}\text{x}=336$
$\Rightarrow\text{x}=\text{Rs. }350$
$\therefore$ CP of the umbrella = Rs. 350
Now, for gain of 4%,
SP = CP + Gain
$\Rightarrow\text{SP}=350+\frac{4}{100}\times350$
$\Rightarrow\text{SP}=350+14$
$\Rightarrow\text{SP}=364$
Hence, in order to gain 4%, the umbrella should be sold for Rs. 364

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Question 254 Marks

The cost price of 12 candles is equal to the selling price of 15 candles. Find the loss percent.

Answer

Let Rs. x be the CP of one candle and Rs. y be the SP of one candle.
Now, CP of 12 candles = SP of 15 candles.
$\Rightarrow 12\text{x} = 15\text{y}$
$\Rightarrow\frac{\text{x}}{\text{y}}=\frac{17}{16}$
Loss = CP - SP
= Rs. x - y
$\therefore$ Loss percentage $=\Big(\frac{\text{loss}}{\text{CP}}\times100\Big)\%$
$=\Big(\frac{\text{x}-\text{y}}{\text{x}}\times100\Big)\%$
$=\Big\{\big(1-\frac{\text{y}}{\text{x}}\big)\times100\Big\}\%$
$=\Big\{\big(1-\frac{12}{15}\big)\times100\Big\}\%$
$=\Big(\frac{3}{15}\times100\Big)\%$
$=20\%$

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4 Mark Question - Maths STD 8 Questions - Vidyadip