The difference between the amount earned and the amount spent where the amount earned exceeds the amount spent is called Profit. In other words, it can also be described as a financial advantage whereas, Loss can simply be defined as when the spending amount exceeds the amount earned. Understanding the differences between Profit and Loss is not only important for Math students but is also a crucial concept for people involved in businesses everywhere.

Mathematically, Profit and Loss can be represented as:

Profit = Selling Price- Cost Price

Loss= Cost Price- Selling Price

Check out the RS Aggarwal Class 7 Solutions Chapter 11 Profit and Loss below:

Q1: Find the SP when:

(i) CP = Rs. 950, gain = 6%

(ii) CP = Rs. 96000, gain = \(16\frac{2}{3}\)%

(iii) CP = Rs. 1540, loss = 4%

(iv) CP = Rs. 8640, loss = \(12 \frac{1}{2}\)%

Sol:

(i) CP = Rs. 950

Gain = 6%

SP = \(\left [\frac {\left ( 100 + Gain \% \right )} {100} \times CP \right ]\) \(= \left [\frac {\left ( 100 + 6 \right )} {100} \times 950 \right ]\) \(= \frac{106}{100} \times 950\) \(= \frac{100700}{100}\)

= Rs. 1007

(ii) CP = Rs. 96000,

Gain = \(16\frac{2}{3} % = Â \frac{50}{3} \)%

SP = \(\left [\frac {\left ( 100 + Gain \% \right )} {100} \times CP \right ]\) \(= \left [\frac {\left ( 100 + \frac{50}{3} \right )} {100} \times 9600 \right ]\) \(= \frac{350}{300} \times 9600\) \(= \frac{3360}{3}\)

= Rs. 11200

(iii) CP = Rs. 1540,

Loss = 4%

SP = \(\left [\frac {\left ( 100 – loss \% \right )} {100} \times CP \right ]\) \(= \left [\frac {\left ( 100 – 4 \right )} {100} \times 1540 \right ]\) \(= \frac{96}{100} \times 1540\) \(= \frac{147840}{100}\)

= Rs. 1478.40

(iv) CP = Rs. 8640

Loss = \(12 \frac{1}{2}% = \frac{25}{2}\)%

SP = \(\left [\frac {\left ( 100 – loss \% \right )} {100} \times CP \right ]\) \(= \left [\frac {\left ( 100 – \frac{25}{2} \right )} {100} \times 8640 \right ]\) \(= \frac{175}{200} \times 8640 \) \(= \frac{1512000}{200}\)

= Rs. 7560

Q2: Find the gain or loss per cent when:

(i) CP = Rs. 24000 and SP = Rs. 2592

(ii) CP = Rs. 1650 and SP = Rs. 1452

(iii) CP = Rs. 12000 and SP = Rs. 12800

(iv) CP = Rs. 1800 and SP = Rs.1611

Sol:

(i) CP = Rs. 2400

Sp = Rs. 2592

Gain = SP – CP = Rs. ( 2592 – 2400) = Rs. 192

Gain % = \(\left ( \frac{Gain}{CP} \times 100 \right ) = \left ( \frac{192}{2400} \times 100 \right ) = 8\)

(ii) CP = Rs. 1650

SP = Rs. 1452

Loss = CP – SP = (1650 – 1452) = Rs. 198

loss % = \(\left ( \frac{Loss}{CP} \times 100 \right ) = \left ( \frac{198}{1650} \times 100 \right ) = 12\)

(iii) CP = Rs. 12000

SP = Rs. 12800

Gain = SP – CP = (12800 – 12000) = Rs. 800

Gain % = \(\left ( \frac{Gain}{CP} \times 100 \right ) = \left ( \frac{800}{12000} \times 100 \right ) = 6.66 \)

(iv) CP = Rs. 1800

SP = Rs.1611

Loss = CP – SP = (1800 – 1611 ) = Rs. 189

loss % = \(\left ( \frac{Loss}{CP} \times 100 \right ) = \left ( \frac{189}{1800} \times 100 \right ) = 10.5 \)

Q3: Find the CP when:

(i) SP = Rs. 924 and gain = 10%

(ii) SP = Rs. 1755, gain = \(12 \frac{1}{2}\)%

(iii) SP = Rs. 8510, loss = 8%

(iv) SP = Rs. 5600, loss = \(6 \frac{2}{3}\)%

Sol:

(i) SP = Rs. 924

Gain = 10%

\(CP = \left [\frac{100}{\left ( 100 + Gain \% \right )} \times SP \right ]\)= \( \left [\frac{100}{\left ( 100 + 10 \right )} \times 924 \right ]\) \(= \frac{92400}{110}\)

= Rs. 840

(ii) SP = Rs. 1755,

Gain = \(12 \frac{1}{2}% = \frac{25}{2} \)%

\(CP = \left [\frac{100}{\left ( 100 + Gain \% \right )} \times SP \right ]\)= \( \left [\frac{100}{\left ( 100 + \frac{25}{2} \right )} \times 1755 \right ]\) \(= \frac{351000} {225}\)

= Rs. 1560

(iii) SP = Rs. 8510

Loss = 8%

\(CP = \left [\frac{100}{\left ( 100 – loss \% \right )} \times SP \right ]\)= \( \left [\frac{100}{\left ( 100 – 8 Â \right )} \times 8510 \right ]\) \(= \frac{851000} {92}\)

= Rs. 9250

(iv) SP = Rs. 5600

Loss = \(6 \frac{2}{3} % = \frac{20}{3} \)%

\(CP = \left [\frac{100}{\left ( 100 – loss \% \right )} \times SP \right ]\)= \( \left [\frac{100}{\left ( 100 – \frac{20}{3} \right )} \times 5600 \right ]\) \(= \frac{168000} {28}\)

= Rs. 6000

Q4: Sudhir bought an almirah for Rs. 13600 and spent Rs. 400 on its transportation. He sold it for Rs. 16800. FInd his gain percent.

Sol:

Cost price of an almirah = Rs. 13600

Transportation cost = Rs 400

Total cost price = Rs. (13600 + 400 ) = Rs. Â 14000

Selling price = Rs. 16800

Now, SP > CP

Gain = SP – CP = (16800 – 14000) = Â Rs. 2800

Gain % = \(\left ( \frac{Gain}{CP} \times 100 \right )%\)

= \(= \left ( \frac{2800}{14000} \times 100 \right )%\)

= 20%

Q5: Ravi purchased an old house for Rs. 765000 and spent Rs. 115000 on its repairs. Then, he sold it at a gain of 5%. Â How much did he get?

Sol:

Cost price of the house = Rs. 765000

Cost of repairing the house = Rs. 115000

Total cost price = (765000 + 115000) = Rs. 880000

Ravi sold it at a gain of 5%

SP = \(\left [\frac{\left ( 100 + Gain \% \right )}{100} \times CP \right ]\)

= \(\left [\frac{\left ( 100 + 5 \right )}{100} \times 880000 \right ]\)

= \(\frac{105}{100} \times 880000\)

= Rs. 924000

Therefore he gets Rs. 924000

Q6: A vendor buys lemon at Rs. 25 per dozen and sells them at the rate of 5 for Rs. 12. Find his gain or loss percent.

Sol:

CP of 12 lemons = Rs. 25

CP of one lemon = Rs. \(\frac{25}{12}\)

CP of five lemons = \(5 \times \frac{25}{12}= \frac{125}{12}\) = Rs. 10.42

SP of five lemons = Rs. 12 Â Â Â Â Â Â Â Â Â Â Â (Given)

Gain = SP – CP = (12 – 10.42) = Rs. 1.58

Gain% = \(\left ( \frac{Gain}{SP} \times 100 \right )\)%

\(= \left ( \frac{1.58}{10.42} \times 100 \right )\)%= 15.2 %

Q7: The selling price of 12 pens is equal to the cost price of 15 pens. Find the gain per cent.

Sol:

Let the cost price of the pen be Re. 1

Cost price of 12 pens = Rs. 12

SP of 12 pens = CP of 15 pens = Rs. 15

Gain = SP – CP = Rs. (15 – 12) = Rs. 3

Gain% = \(\left ( \frac{Gain}{SP} \times 100 \right )\)%

\(= \left ( \frac{3}{12} \times 100 \right )\)%= 25 %

Therefore Gain % = 25%

Q8: The selling price of 16 spoons is equal to the cost price of 15 spoons. Find the loss per cent.

Sol:

Let the cost price of one spoon be Re. 1

CP of 16 spoons = Rs. 16

SP if 16 s poon = CP of 15 spoons = Rs. 15

Loss = CP – SP = (16 – 15) = Re. 1

Loss% = \(= \left ( \frac{Loss}{CP} \times 100 \right )\)%

\(= \left ( \frac{1}{16} \times 100 \right )\)= 6.25%

Loss% = 6.25%

Q9: Manoj purchased a video for Rs. 12000. He sold it to Rahul at a gain of 10%. If Rahul sells it to Rakesh at a loss of 5%, what did Rakesh pay for it?

Sol:

Cost price of a video = Rs. 12000

SP of a video at a gain of 10% = \(\left [\frac{\left ( 100 + Gain \% \right )}{100} \times CP \right ]\)

= \(\left [\frac{\left ( 100 + 10 \right )}{100} \times 12000 \right ]\)

= \(\left [\frac{\left ( 110 \right )}{100} \times 12000 \right ]\)

= Rs. 13200

So, Rahul purchased at a cost price of Rs. 13200.

Rahul sells it at a loss of 5%.

SP of a video at loss of 5% = \(\left [\frac{\left ( 100 â€“ loss \% \right )}{100} \times CP \right ]\)

= \(\left [\frac{\left ( 100 – 5 \right )}{100} \times 13200 \right ]\) \(= \frac{95}{100} \times 13200\)

= Rs. 12540

Therefore, Rakesh pays Rs. 12540

Q10: On selling a sofa-set for Rs. 21600, a dealer gains 8%. For how much did he purchase it?

Sol:

SP of the sofa set = Rs. 21600

Gain% = 8

CP of a sofa set = \(\left [\frac{100}{\left ( 100 + Gain \% \right )} \times SP \right ]\) \(= \left [\frac{100}{\left ( 100 + 8 \right )} \times 21600 \right ]\)

= \(\frac{2160000}{108}\)

= Rs. 20000

He purchased it at the cost of Rs. 20000.

Q11: On selling a watch for Rs. 11400, a shopkeeper loses 5%. For how much did he purchase it?

Sol:

SP of the watch = Rs. 11400

Loss% = 5

CP = \(\left [\frac{100}{\left ( 100 â€“ Loss \% \right )} \times SP \right ]\)

= \(\left [\frac{100}{\left ( 100 – 5 \right )} \times 11400 \right ]\)

= \(= \frac{11400}{95}\)

= Rs. 12000

He purchased it at the cost of Rs. 12000.

Q12: On selling a calculator for Rs. 1325, a man gains 6%. For how much should he sell it to gain 12%?

Sol:

SP of the calculator = Rs. 1325

Gain% = 6

CP of the calculator = \(\left [\frac{100}{\left ( 100 + Gain \% \right )} \times SP \right ]\)

= \(\left [\frac{100}{\left ( 100 + 6 \right )} \times 1325 \right ]\)

= \(\frac{132500}{106}\)

=Rs. 1250

SP of the calculator = \(\left [\frac{\left ( 100 + Gain \% \right )}{100} \times CP \right ]\)

= \(\left [\frac{\left ( 100 + 12 \right )}{100} \times 1250 \right ]\)

= \(\frac{140000}{100}\)

= Rs. 1400

Q13: On selling a computer for Rs. 24480, a dealer loses 4%. For how much should he sell it to gain 4%?

Sol:

SP of a computer = Rs. 24480

Loss% = 4

CP of the computer = \(\left [\frac{100}{\left ( 100 â€“ Loss \% \right )} \times SP \right ]\)

= \(\left [\frac{100}{\left ( 100 – 4 \right )} \times 24480 \right ]\)

= \(\frac{2448000}{96}\)

= Rs. 25500

In order to gain 4%,

SP of the computer = \(\left [\frac{\left ( 100 + Gain \% \right )}{100} \times CP \right ]\)

= \(\left [\frac{\left ( 100 + 4 \right )}{100} \times 25500 \right ]\)

= \(\left [\frac{104}{100} \times 25500 \right ]\)

= Rs. 26520

Q14: A tricycle is sold at a gain of 15%. Had it been sold for Rs.108 more then the profit would have been 20%. Find the cost price.

Sol:

Let the CP of the tricycle be Rs. x

SP at 15% gain = \(\left [\frac{\left ( 100 + Gain \% \right )}{100} \times CP \right ]\)

= \(\left [\frac{\left ( 100 + 15 \right )}{100} \times x \right ]\)

= \(\frac{115}{100} x\)

= Rs. \(\frac{23}{20} x\)

SP at 20% gain = \(x \times \frac{120}{100} = Rs. \frac{6}{5} x\) \(\frac{6}{5} x – \frac{23}{20} x = 108\) \(\Rightarrow \frac{24x – 23x }{20} = 108\) \(\Rightarrow \frac{x}{20} = 108\) \(\Rightarrow x = 2160 \)

Hence, the cost price of the tricycle is Rs. 2160

Q15: Sandeep sold a television at a loss of 8%. If it had been sold for Rs. 3360 more, he would have gained 6%. For how much did Sandeep buy it?

Sol:

Let CP of a television be Rs. x.

SP of 8% loss = \(\frac{\left ( 100 – 8 \right )}{100} \times x = Rs. \frac{92}{100}\) x

SP at 6% gain = \(\frac{\left ( 100 + 6 \right )}{100} \times x = Rs. \frac{106}{100}\) x

\(\frac{106}{100} x – \frac{92}{100} x = 3360\) \(\Rightarrow \frac{14}{100} x = 3360\) \(\Rightarrow x = \frac{336000}{14} = 24000\)Therefore, CP = Rs. 24000

Sandeep bought it at the cost of Rs. 24000.

Q16: Pankaj sells two cycles for Rs. 2376 each. On one he gains 10% and on the other, he loses 10%. Find his gain or loss percent.

Sol:

SP of each cycle = Rs. 2376

He gains 10% in one cycle.

CP = \(\left [\frac{100}{\left ( 100 + Gain \% \right )} \times SP \right ]\)

= \(\left [\frac{100}{\left ( 100 + 10 \right )} \times 2376 \right ]\)

= \(\frac{100}{110} \times 2376\)

= Rs. 2160

He looses 10% in the second cycle.

CP = \(\frac{100}{100 – loss \%} \times SP\)

= \(\frac{100}{100 – 10} \times 2376 \) \(\frac{100}{90} \times 2376\)

= \(\frac{23760}{9}\)

Rs. 2640

Total CP = Rs. (2160 Â + 2640) = Rs. 4800

Total SP = Rs. (2376 + 2376) = Rs. 4752

Loss = CP – CP = Rs. (4800 – 4752) = Rs. 48

loss % = \(\left ( \frac{Loss}{CP} \times 100 \right ) %\) \(= \left ( \frac{48}{4800} \times \right )\) %

= 1%

Q17: On selling an exhaust fan for Rs. 7350, a man gains \(\frac{1}{6}\) ot its cost price. Find the cost price of the fan.

Sol:

Let the CP of the exhaust fan be Rs. x.

Gain = Rs. \(\frac{x}{6}\)

SP = Rs. \(\left ( x + \frac{x}{6} \right )\)

SP = Rs. 7350

Therefore, \(x + \frac{x}{6} = 7350\) \(\Rightarrow \frac{7}{6} x = 7350\) \(\Rightarrow x = \frac{7350 \times 6 }{7} = \frac{44100}{7} = 6300\)

CP of the fan = Rs. 6300

Q18: Mohit sold a watch to Karim at a gain of 10% and Karim sold it to Rahim at a gain of 4%. If Rahim pays Rs. 14300 for it, for how much did Mohit purchase it?

Sol:

Mohit sold a watch to Karim at Rs. x.

Mohit sold it at a gain of 10%

SP of the watch = 110% of x

\(= \left ( x + \frac{110}{100} \right ) = Rs.Â \frac{11}{20} x\)Karim sold it to Rahim at a gain of 4%.

SP of the watch = 14% of \(\frac{11}{10} x\) = \(\left ( \frac{104}{100} \times \frac{11}{10} x \right )\)= Rs. \(\left ( \frac{26}{25} \times \frac{11}{10} \times x \right )\)

But Rahim pays Rs. 14300

Therefore, \(\frac{26}{25} \times \frac{11}{10} x = 14300\) \(\Rightarrow x = \frac{14300 \times 25 \times 10}{26 \times 11} = \frac{3575000}{286} = 12500\)

Mohit purchased it at Rs. 25000.

Q19: If the manufacturer gains 10%, the wholesale dealer 15% and retailer 25% then what is the production cost of a washing machine whose retail price is Rs. 37950?

Sol:

Let the production cost a washing machine be Rs. x.

Profit of the manufacturer = 10%

SP of the manufacturer = 110% of x

\(= \left ( x + \frac{110}{100} \right ) = \frac{110}{100} x = Rs. \frac{11}{10}\)Profit of the wholesale dealer = 15%

SP of the wholesale dealer = 115% of Rs. \(\frac{11}{10} x\)

= Rs. \(\left ( \frac{11}{10} x \times \frac{115}{100} \right ) = Rs.Â \left ( \left ( \frac{11}{10} x \times \frac{23}{20} \right ) \right )\)

Profit of the retailer = 25%

SP of the retailer = 125% of Rs. \(\left ( \frac{11}{10} x \times \frac{23}{20} \right )\)

= Rs. \(\left ( \frac{11}{10} x \times \frac{23}{20} \times \frac{125}{100} \right )\) = Rs. \(\left ( \frac{11}{10} x \times \frac{23}{20} \times \frac{5}{4} \right )\)

Given:

Retail price = Rs. 37950

Therefore, \(\left ( \frac{11}{10} x \times \frac{23}{20} \times \frac{5}{4} \right ) = 37950\) \(\Rightarrow x = \frac{37950 \times 10 \times 20 \times 4}{11 \times 23 \times 5}\) \(\Rightarrow x = \frac{30360000}{1265} = 24000\)

Therefore, Production cost of a washing machine = Rs. 24000

Q20: Mr Mehta purchased a video for Rs. 20000 and a television for Rs. 30000. On the video he lost 5% and on the television he gained 8%. Find the total gain or loss per cent.

Sol:

Mr. Mehta purchased a video at the cost of Rs. 20000.

Mr. Mehta purchased a television at the cost of Rs. 30000.

Total cost = Rs. (20000 + 30000) = Rs. 50000

He lost 5% on the video .

SP = \(\frac{\left ( 100 – loss \% \right )}{100} \times CP\)

= \(\frac{\left ( 100 – 5 \right )}{100} \times 20000 \)

= \(\frac{95}{100} \times 20000 \)

= Rs. 19000

He gained 8% on the television.

SP = \(\frac{\left ( 100 + Gain \% \right )}{100} \times CP\)

= \(\frac{\left ( 100 + 8 \right )}{100} \times 30000 \) \(\frac{108}{100} \times 30000 \)

= Rs. 32400

Total SP = Rs. (19000 + 32400) = Rs. 51400

Total CP = Rs. 50000

Total Gain = SP – CP = Rs. (54100 – 5000) = Rs. 1400

Gain% = \(\left ( \frac{Gain}{CP} \times 100 \right )\)%

= \(\left ( \frac{1400}{50000} \times 100 \right )\)

= 2.8%

Q21: By selling 36 oranges, a vendor suffers a loss equal to the selling price of 4 oranges. Find his loss per cent.

Sol:

Let the CP of 1 orange be Rs. x

Therefore, CP of 36 oranges = Rs. 36x

Let SP of orange be Rs. y

Therefore, SP of 36 oranges = Rs. 36y

Loss = SP of 4 oranges = 4y Â Â Â Â Â Â (given)

We know :

Loss = CP – SP

\(\Rightarrow 4y = 36x – 36y \) \(\Rightarrow 4y + 36y = 36x \) \(\Rightarrow 40y = 36 x\) \(\Rightarrow 10y = 9 x\) \(\Rightarrow y = \frac{9}{10} x\)loss % = \(\left ( \frac{Loss}{CP} \times 100 \right )\)%

\(= \left ( \frac{4y}{36x} \times 100 \right )\) \(= \left ( \frac{4 \times 9x}{36x \times 10} \times 100 \right )\)= 10%

Loss = 10%

Q22: By selling 8b dozen pencils, a shopkeeper gains the selling price of one dozen pencils. Find his gain per cent.

Sol:

Let the CP of one pencil be Rs. x

Therefore, the CP of 96 pencils will be Rs. 96x.

Let SP of one pencil be Rs. y.

Gain = SP of one dozen pencil = Rs. 12y Â Â Â Â Â (given)

Gain = SP – CP

\(\Rightarrow 12y = 96 y – 96 x\) \(\Rightarrow 96 x = 96 y – 12 y\) \(\Rightarrow 96 x = 84 y\) \(\Rightarrow x = \frac{84y}{96}\)Gain % = \(\left ( \frac{Gain}{CP} \times 100 \right )%\) \(= \left ( \frac{12y}{96x} \times 100 \right )%\) \(= \left ( \frac{12 y \times 96}{96 \times 84y} \times 100 \right )%\)

= 14.28 %