Profit and loss questions

\( \% gain = \frac{Error}{True value-Error} \times 100 = \frac{40}{1000-40} \times 100 = \frac{100}{24} = 4\frac{1}{6} \% \)

The original price of the rice = \( \frac{30\times 60}{3\times (100-30)} = \frac{600}{70} = 8\tfrac{4}{7} \)

\(\frac{a-b}{b}=\frac{20-15}{15}\times100=\frac{5}{15}\times100=\frac{100}{3}=33\frac{1}{3}\%\)

Total S.P. = Rs. 8000 and

Total C.P. = Rs. 8000

S.P. of 1st commodity = Rs. 4000

Gain on it = 25%

∴ C.P. of 1st commodity=Rs.(\(\frac{100}{125}×4000\))=Rs.3200

C.P. of 2nd commodity=Rs.(8000−3200)=Rs.4800

S.P. of 2nd commodity=Rs.4000

∴loss on 2nd commodity=(\(\frac{800}{4800}\)×100)%=\(16\frac{2}{3}\)%

Let the original price be x, then
30% of x = 82.50
x = \(\frac{82.5}{30}\) \(\times\) 100 = Rs. 275
Deepa bought calculator in 275 – 82.50 = Rs. 192.50

Let the CP = 100

After allowing a discount of 10% the SP will be = 90

Ramu bought the article at 20% discount on Labelled Price.

80% of Labelled price = 100

Labeled Price = 125

Now, loss in value if the item was bought at LP = LP – SP

= 125 – 90 = 35

Loss % = \(\frac{35}{125} \times 100\)

= 28 %

Calculation :

• The cost price of the article \(\displaystyle= \frac{SP\times 100 }{ ( 100 – Loss\%)} \)

  \(\displaystyle= \frac{1512\times 100 }{ ( 100 – 5.5)} \)

  \(\displaystyle= \frac{1512\times 100 }{ ( 94.5)} \)

  \(=Rs. 1600\)

• \(M.P. = \displaystyle\frac{(100 + Gain\%)}{(100 – Discount\%)} × C.P.\)

  = \(\frac{100+20}{100-20}\times1600 \)

  = \(\frac{120}{80}\times1600 \)

  =Rs. 2400

• Hence, the answer is option A

C.P of 15 books = S.P of 12 books.

1st discount = \(\dfrac{600\times20}{100} = 120\)
2nd discount = 600 - 320 - 120
= 160
2nd discount = \(\dfrac{160}{480} \times 100\)
= 33.33%

Let cost price of article be Rs x

(15+5)% of x = 1050

20% of x = 1050

x = 5250

SP = 125% of 5250 = 6562.5

• Normally we can buy x kg for 30 rupees. Then price of 1 kg will be \(\frac{30}{x}\).

• After reduction we can buy x+3 kg for 30 rupees.

• Reduction is 30%, then price of 1 kg will be 0.7\(\times\frac{30}{x}\).

• \(0.7\times\frac{30}{x}(x+3)\) = 30

• on solving, x= 7

• Original price = \(\frac{30}{7}\) = \(4\frac{2}{7}\) rupees

• Reduced price = \(0.7 \times\frac{30}{7}\) = 3 rupees

Let the Cost Price be Rs.100x

Loss = 20%

Then, Selling Price = 80% of Rs.100x = Rs.80x

Given, 80x = Rs.480

=> x = Rs.6

Then, Cost Price = Rs.100x = Rs.600

Required profit = 20%

Then, Selling Price = 120% of Rs.600 = Rs.720.

Let's denote the cost price of the article as CP.

In the first scenario, the shopkeeper sells the article at a 10% profit.

In the second scenario, if the shopkeeper had bought the article at 8% less and sold it for Rs. 8 more, he would have gained a 20% profit.

Let's calculate the selling price (SP) ,

First scenario (10% profit):Selling Price (SP1) = CP + 10% of CP = CP + 0.1 CP = 1.1 CP

Second scenario (20% profit with adjusted cost price and selling price): Let's denote the adjusted cost price as "CP2" (8% less than the original CP): CP2 = CP - 0.08 CP = 0.92 CP

The selling price (SP2) in this scenario will be: SP2 = CP2 + 20% of CP2 = CP2 + 0.2 CP2 = 1.2 CP2

Given that the selling price is Rs. 8 more in the second scenario, we can set up an equation: SP2 - SP1 = Rs. 8 1.2 CP2 - 1.1 CP = 8

Substitute the value of CP2 from the equation for adjusted cost price: 1.2 (0.92 CP) - 1.1 * CP = 8

Now solve for CP: 1.104 CP - 1.1 CP = 8 0.004 * CP = 8 CP = 8 / 0.004 CP = 2000

So, the cost price of the article is Rs. 2000.

Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.

New C.P. = 125% of Rs. 100 = Rs. 125

New S.P. = Rs. 420.

Profit = Rs. (420 - 125) = Rs. 295.

Required percentage =\(\frac{295}{420} \times 100 = 70\%\)

Given:

Cost price of 100 Trains \(=\) Selling price of 60 Trains

Profit percentage \(=\{( SP - CP ) / CP \} \times 100\)

Let CP of each train = Rs. 1

CP of 60 Trains \(=\) Rs. 60

Their \(SP =\) Rs. 100

Gain \(=\) Rs. \((100-60)=\) Rs. 40

Gain \(\%=40 / 60 \times 100=66.67 \%\)

\(\therefore\) Gain \(\%\) is \(66.67 \%\).

CP of first article =

\( \frac{17250\times 100}{115}\)

Profit from first article = 17250 – 15000 = Rs. 2250

A.T.Q.,

CP of second article =

\( 2250\times \frac{100}{10}\)

SP of second article = 22500 × 90% = Rs. 20250

Let the cost price of the television set be Rs. x
Then, (100 + 16)% = 16588
100% = x
By the cross multiplication, we get
x = \(\frac{16588\times100}{116}\) = Rs. 14300

Let C.P. = Rs 100
Loss = 10% of 100 = Rs 10 and S.P. = Rs (100 - 10) = Rs 90
When S.P. = Rs 90, C.P. = Rs 100
When S.P. = Rs. 1, C.P. = Rs \(\frac{100}{90}\)
When S.P. = Rs 270, C.P. = \(\frac{100}{90}\) \(\times\) 270
\(\Rightarrow\) C.P. = Rs 300

• Let the original price be Rs. \(x\).
• Reduced price =\( x – 20 \% \ of \ x = x – 0.2x = 0.8x\).

• According to the question,

  \(\Rightarrow \frac{450}{0.8x}-\frac{450}{x}\)=50

  \(\Rightarrow \frac{1125}{2x} -\frac{450}{x}\) = 50

  \(\Rightarrow \frac{1125-900}{2x}\) = 50

  \(\Rightarrow \frac{225}{2x}\) = 50

  \(\Rightarrow x = \frac{225}{100}\)

  = Rs. 2.25/ kg.

• Hence option B is the answer.

Cost price of 100 eggs,C.P. =\(100\times 6 = 600\:\)Rs
Selling price of 1st 25 eggs = \(25\times 6\times \frac{110}{100} = 165\:\)Rs
Selling price of 2nd 25 eggs = \(25\times6\times \frac{75}{100}= 112.5\:\)Rs
Selling price of balance 50 eggs =\(50\times 6\times \frac{120}{100}=360\: \)Rs
Selling price of 100 eggs,S.P. = \(165+112.5+360 = 637.5\)Rs
Profit percentage = \(\frac{S.P-C.P}{C.P}\times 100= \frac{637.5-600}{600}\times100= \frac{37.5}{6} = 6.25\)%

C.P. of 12 eggs = Rs. 16
50% gain = 150% of 16 = 24.
S.P. of 12 eggs = \(\frac{24}{12}\) = Rs. 2

CP for B = 120% of 400
= \(\frac{120}{100}\) \(\times\)100 = Rs. 480
CP for C = 110% of 480
\(\frac{110}{100}\) \(\times\)480 = Rs. 528

\(\mathrm{X}\) can buy \(5 \mathrm{~kg}\) more rice for Rs. 100

Then, \(X\) can buy \(1 \mathrm{~kg}\) more rice for Rs. 20

Then, Reduced price \(=R s .20 \times \frac{20}{100}=R s .4\)

% gain = \(\frac{error}{ True value - error } \times 100 \)

= \(\frac{60}{ 1000 - 60 } \times 100 \)

=\(\frac{60}{ 940 } \times 100 \)

= \(6.38 \%\)

Let C.P =Rs. 100 Then, S.P=Rs.120 Let M.P be Rs.x , Then, \(90\% of x=120\) \(x=(\frac{120\times 100}{90})=133\frac{1}{3}\) Marked price = \(33\frac{1}{3}\%\) above C.P

Let the cost price of the cell phone be x, then,
128% of x = 8960
x \(\times\) \(\frac{128}{100}\) = 8960
\(\Rightarrow\) x = Rs. 7000

According to the question,

Let the previous rate of rice is Rs. x/kg.

Now the new rate of rice is

= x × \(\frac{80}{100}\)

= \(\frac{4}{5}\)x

Now in Rs. 800 the customer purchased more 12.5 kg,

= \(800\frac{4}{5}\) x− \(\frac{800}{x}\)=12.5

= \(\frac{4000}{4x}\)− \(\frac{800}{x}\)=12.5

= \(\frac{200}{x}\)=12.5

=x= \(\frac{200}{12.5}\)

= 16

Hence, the correct option is (D).

Given;

Amount of Profit = Amount of Loss

\(\Rightarrow 8800-\) Cost \(=\) Cost \(-7200\)

\(\Rightarrow 2 \times \cos t=8800+7200\)

\(\Rightarrow\) Cost \(=\frac{16000}{2}=Rs. 8000\)

Now, profit (in case of \(S P=Rs. 9600)=9600-8000=Rs. 1600\)

Profit (in \%) \(=\frac{1600}{8000} \times 100=20 \%\).

Let the sold price of the article \(=100\)

Therefore , selling price when there is the loss of \(20 \%=\) Rs. 75

Cost price of the article \(=75 \times \frac{100}{60}=125\)

When article is sold at original price \(=\frac{125-100}{100} \times 100=25 \%\) loss

There is the loss of \(25 \%\) when sold at original price.

So we have C.P = 27.50
S.P = 28.60
Gain = S.P -C.P = 28.60 - 27.50 = 1.10
Gain percentage = (\(\frac{gain}{cost} \times 100)\)%
= \((\frac {1.10}{27.50} \times 100)\)% = 4%

• Given, the marked price of Jeans is = 1000
• Anu bought the jeans at Rs. 714
• The first discount is given, to be = 16%
• Let the second discount be = x %

• Then, 84% of (100 - x)% of 1000 = 714

  \(\Rightarrow \frac{84}{100}\times \frac{\left ( 100-x \right )}{100}\times 1000= 714\)

  \(\Rightarrow 8400 - 84x = 714\times 10\)

  \(\Rightarrow 84x = 8400 - 7140\)

  \(\Rightarrow x = \frac{1260}{84} \)

  \(\therefore x = 15 \)

• Therefore the second discount is 15%

C.P of an article is Rs. 390

Profit% = 3.12%

\(SP = CP + profit\% \times CP\)

\(\rightarrow SP = 390 + 3.12\% \times 390\)

\(\rightarrow SP = 390 + 0.0312 \times 390\)

\(\rightarrow SP = Rs. 402.168 \approx Rs. 402\)

Let a number x to compare the assumed selling price and actual selling price.

123 \(\times \) x =7011

x = 57

That means if we multiply the assumed value with 57, we get the original selling price.

So, multiply the cost price with 57 to get the original cost price, i.e., 100 \(\times \) 57 = 5700.

S.P=23680, profit = 28% , C.P=\((\frac{100}{128}\times 23680)=Rs.18500.\)

Given that, MP = 630

Let \(x\) be the second discount.

\(630\times\frac{80}{100}\times\frac{100-x}{100}=420\)

\(100 - x=83.33\)

\(x\) = 16.66%.

20% loss = 100−20 = 80%

80% = 400

25% profit = 100 + 25 = 125

125% = \( \frac{400}{80}× 125 \)= Rs. 625

Let the C.P of the article be Rs 1 per gram
C.P of 900gm = Rs 900,
S.P of 900gm = Rs 1000,
Gain % = \(\frac{100}{900}\times 100 \)% = \(11\frac{1}{9}\)%

\( \frac{100}{90} \) x 240 x \( \frac{120}{100}\) = 320

CP = 100%

Loss = 10% \(\Rightarrow\) SP = 90%

90% + 75 = 105%

15% = 75

1% = 5 \(\Rightarrow\) 100% = 500

CP = 500

SP when it is sold at 15% profit = 500 + 15% of 500

= 500 + 75 = 575.

Cost price of ten books = Rs.10

Then cost price of a book = Rs.1

Selling price of 9 books = Rs.10

Selling price of a book = \(\frac{10}{9}\) Rs

Then selling price of 10 books = \(10 \times \frac{10}{9}\) = 100/9

Profit = 100/9 - 10 = 10/9

Profit percentage = \(\frac{10/9}{1}\times 100\) = 100/9 = \(11 \frac{1}{9}\)%

Let the cost price be \(x\) \(\frac{110x}{100}-\frac{80x}{100}=600\)
\(30x=60000\) and \(x=Rs 2000\)