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

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%

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

= \( \left [\frac{100}{\left ( 100 – 8 \right )} \times 8510 \right ]\)

\(= \frac{851000} {92}\)

= 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. 14000

Selling price = Rs. 16800

Now, SP > CP

Gain = SP – CP = (16800 – 14000) = 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%. 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 (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% = \(\left [\frac{\left ( 100 – loss \% \right )}{100} \times CP \right ]\)

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

\(= \frac{95}{100} \times 13200\)

= 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 = \(\left [\frac{100}{\left ( 100 – Loss \% \right )} \times SP \right ]\)

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

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

= 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 = \(\left [\frac{100}{\left ( 100 – Loss \% \right )} \times SP \right ]\)

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

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

= 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 + 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

\(= \left ( x + \frac{110}{100} \right ) = Rs. \frac{11}{20} x\)

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

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 (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 pencils be Rs. y.

Gain = SP of one dozen pencil = Rs. 12y (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 %