## Profit and Loss

1. A man bought a book for Rs.450 and sold for Rs.495. Find the gain percent.

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;S.P.&space;=&space;495$         $\par&space;C.P.&space;=&space;450$

$\par&space;Gain&space;=&space;495&space;-&space;450&space;=&space;45$                       $\lbrack&space;gain&space;=&space;S.P&space;-&space;C.P.\rbrack&space;$

$\par&space;Gain$ % $=\frac{45}{450}&space;\times&space;&space;100&space;=&space;10$                    $\par&space;\lbrack&space;gain$ % $=&space;\frac{Gain}{C.P.}&space;\times&space;100\rbrack$

$\par&space;\therefore&space;gain$ % $=&space;10$			
2. A man bought a cycle for Rs.450 and sold for Rs.405. find the loss percent.

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;Loss&space;=&space;450&space;-&space;405&space;=&space;45$                                   $&space;\qquad&space;\lbrack&space;loss&space;=&space;C.P.&space;-&space;S.P.\rbrack&space;$

$\par&space;Loss$ %  $=&space;\frac{45}{450}&space;\times&space;100&space;=&space;10$                                 $\par&space;\lbrack&space;loss$ % $=&space;\frac{loss}{C.P.}&space;\times&space;100\rbrack&space;$

$\par&space;\therefore&space;loss$ % $=&space;10$			
3. A man bought an object for Rs.750 and sold for 10% gain. Find S.P.

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;C.P.&space;=&space;750$                $\par&space;gain&space;=&space;10%$%

$S.P.&space;=&space;750&space;\times&space;\frac{100&space;+&space;10}{100}$                $\lbrack&space;S.P.&space;=&space;C.P.\times&space;\frac{100&space;+&space;gain\%}{100}\rbrack$

$750&space;\times&space;\frac{110}{100}&space;=&space;825$

$\par&space;\therefore&space;S.P.&space;=&space;825$			
4. A radio is bought for Rs.750 and sold for 4% loss. Find S.P.

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;C.P.&space;=&space;750$           $\par&space;loss&space;=&space;4\%$

$\par&space;S.P.$ $=&space;750&space;\times&space;\frac{100&space;-&space;4}{100}$                                                               $\par&space;\lbrack&space;S.P$$=&space;C.P.&space;\times&space;\frac{100&space;-&space;loss&space;\%}{100}\rbrack$

$750&space;\times&space;\frac{96}{100}&space;=&space;360$

$\therefore&space;S.P.$ $=&space;360$			
5. A chair is sold for Rs.825. gain is 10%. find C.P.

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;S.P.&space;=&space;825$         $\par&space;gain&space;=&space;10\%$

$\par&space;C.P$. $=&space;825&space;\times&space;\frac{100}{100&space;+&space;10}$                                                            $\par&space;\lbrack&space;C.P.$ $\par&space;=&space;S.P.$  $\times&space;\frac{100}{100&space;+&space;gain\%}\rbrack$

$825&space;\times&space;\frac{100}{110}&space;=&space;750$

$\therefore$ $\par&space;C.P.$  $=&space;750$			
6. If a man sold a clock at Rs.144 he will get 10% loss. To get 15% gain at what price he has to sell the clock ?

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;S.P.&space;=&space;144$        $\par&space;loss&space;=&space;10\%$
$\par&space;C.P.$ $=&space;144&space;\times&space;\frac{100}{100&space;-10}$                                                           $\par&space;\lbrack&space;C.P.&space;=&space;S.P.$ $\times&space;\frac{100}{100&space;-&space;loss\%}\rbrack$
$144&space;\times&space;\frac{100}{90}&space;=&space;160$
$\par&space;Required&space;S.P.&space;=&space;15\%$
$\par&space;S.P.&space;=$ $160&space;\times&space;\frac{100&space;+&space;15}{100}$
$160&space;\times&space;\frac{115}{100}&space;=&space;184$			
7. A man bought a house for Rs.3750 and spent Rs.600 on repairs and sold for Rs.5000. what is Gain percent ?

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;C.P.&space;of&space;house$ $=&space;3750$
$\par&space;Expenses&space;on&space;repairs&space;=$ $600$
$\par&space;Total&space;cost&space;of&space;house&space;=&space;3750&space;+&space;600&space;=&space;4350$
$\par&space;S.P.&space;=&space;5000$
$\par&space;Gain&space;=&space;5000&space;-&space;4350&space;=&space;650$
$\par&space;Gain\%&space;=$ $\frac{650}{4350}&space;\times&space;100&space;=&space;14.9$			
8. A man bought a horse for Rs.400 and cart for Rs.250. He sold cart at 20% profit and horse at 4% loss. Find gain or loss percent.

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;C.P.&space;of&space;horse&space;=&space;400$              $\par&space;loss&space;=&space;4\%$
$\par&space;S.P.&space;=$ $400&space;\times&space;\frac{100&space;-&space;4&space;}{100}&space;=&space;400&space;\times&space;\frac{96}{100}&space;=&space;384$
$\par&space;C.P.&space;of&space;cart&space;=&space;250$                $\par&space;gain&space;=&space;20\%$
$\par&space;S.P.&space;=$ $250&space;\times&space;\frac{100&space;+&space;20}{100}&space;=&space;250&space;\times&space;\frac{120}{100}&space;=&space;300$
$\par&space;C.P.&space;of&space;horse&space;and&space;cart&space;=&space;400&space;+&space;250&space;=&space;650$
$\par&space;S.P.&space;of&space;horse&space;and&space;cart&space;=&space;384&space;+&space;300&space;=&space;684$
$\par&space;Gain&space;=&space;684&space;-&space;650&space;=&space;34$as
a$\par&space;Gain\%&space;=$ $\frac{34}{650}&space;\times&space;100&space;=&space;\frac{340}{65}&space;=&space;5.23$			
9. Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800 his gain percentage is

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;C.P.&space;=&space;(4700&space;+&space;800)&space;=&space;Rs.&space;5500$
$\par&space;S.P.&space;=&space;Rs.&space;5800$
$\par&space;Gain\%&space;=$ $(\frac{300}{5500}\times&space;100)&space;=&space;5\frac{5}{11}\%$			
10. A shopkeeper purchased 70 kg of potatoes for Rs.420 And sold the whole lot at the rate of Rs. 6.50 per kg. What Will be his gain percent ?

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;C.P.&space;of&space;1&space;kg&space;=$ $\par&space;Rs.$$(\frac{420}{70})$  $=$ $\par&space;Rs.&space;6$
$\par&space;S.P.&space;of&space;1&space;kg&space;=$ $\par&space;Rs.&space;6.50$
$\par&space;Gain\%&space;=$  $(\frac{0.50}{6}\times&space;100)\%&space;=&space;\frac{25}{3}\%&space;=&space;8\frac{1}{3}\%$			
11. Sam purchased 20 dozens of toys at the rate of Rs. 375 Per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit ?

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;C.P.&space;of&space;1&space;toy&space;=&space;Rs.$  $\left&space;(&space;\frac{375}{12}&space;\right&space;)$ $\par&space;=&space;Rs.&space;31.25$
$\par&space;S.P.&space;of&space;1&space;toy&space;=&space;Rs.33$
$\par&space;Profit\%&space;=$ $\left(\frac{1.75}{31.25}\times&space;100\right)\%$  $=&space;\frac{28}{5}\%&space;=&space;5.6\%$			
12. 100 oranges are bought at the rate of Rs.350 and sold at the rate of Rs. 48 per dozen. The percentage of profit or loss is

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;C.P.&space;of&space;1&space;orange&space;=&space;Rs.$ $\left(\frac{350}{100}\right)&space;=$  $\par&space;Rs.&space;3.50$
$\par&space;S.P.&space;of&space;1&space;orange&space;=&space;Rs.$ $\left(\frac{48}{12}\right)&space;=$  $\par&space;Rs.&space;4$
$\par&space;Gain\%&space;=$ $\left(\frac{0.50}{3.50}\times&space;100)\right)\%$  $=&space;\frac{100}{7}\%&space;=$ $14\frac{2}{7}\%$			
13. A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle ?

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;S.P.&space;=&space;58\%&space;of&space;Rs.&space;1400&space;=&space;Rs.$ $\left(\frac{120}{100}\times&space;400)\right)&space;=$  $\par&space;Rs.&space;1190$
14. A sells an article which costs him Rs. 400 to B at a profit of 20%. B then sells it to C, making a profit of 10% on the price he paid to A. How much does C pay B ?

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;C.P.&space;of&space;B&space;=&space;120\%&space;of&space;Rs.&space;400&space;=&space;Rs.$ $\left(\frac{120}{100}\times&space;400)\right)&space;=$ $\par&space;Rs.&space;480$
$\par&space;C.P.&space;for&space;C&space;=&space;110\%&space;of&space;Rs.&space;480&space;=&space;Rs.$$\left(\frac{110}{100}\times&space;480)&space;\right)=$ $\par&space;Rs.&space;528$			
15. Uday purchased a machine for Rs. 80,000 and spent Rs. 5000 on repair and Rs.1000 on transport and sold it with 25% profit. At what price did he sell the machine ?

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;C.&space;P.&space;=&space;(80000&space;+&space;5000&space;+&space;1000)&space;=&space;Rs.&space;86000$as
as$\par&space;Profit&space;=&space;25\%$
$\par&space;S.P.&space;=&space;125\%&space;of&space;Rs.86000&space;=&space;Rs.$ $\left(\frac{125}{100}\times&space;86000)\right)&space;=$  $\par&space;Rs.&space;107500$			
16. By selling an article for Rs. 100, a man gains Rs. 15. Then his gain percent is

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;S.P.&space;=&space;Rs.&space;100,&space;gain&space;=&space;Rs.&space;15$

$\par&space;C.P.&space;=&space;Rs.&space;(100&space;-&space;15)&space;=&space;Rs.&space;85$

$\par&space;Gain\%&space;=$ $\left(\frac{15}{85}\times&space;100)\right)\%&space;=$  $\frac{300}{17}\%&space;=$ $17\frac{11}{17}\%$			
17. When a commodity is sold for Rs. 34.80, there is a loss of 2%. What is the cost price of the commodity ?

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;C.P.&space;=&space;Rs.$ $\left(\frac{100}{75}\times&space;34.80)\right)&space;=$  $\par&space;Rs.&space;46.40$
18. A shopkeeper expects a gain of 22 1/2% on his cost price. If in a week, his sale was of Rs. 392, what was his profit ?

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;C.P.&space;=&space;Rs.$ $\left(\frac{100}{122.50}\times&space;392)\right)$

$\par&space;=&space;Rs.$ $\left(\frac{1000}{1225}\times&space;392)\right)$

$\par&space;=&space;Rs.&space;320$
$\par&space;Profit&space;=&space;Rs.&space;(392&space;-&space;320)&space;=&space;Rs.72$			
19. The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is

A. 620

B. 680

C. 720

D. 750

Explanation:

			$\par&space;S.P.&space;=&space;Rs.$ $\left(\frac{616&space;\times&space;100}{110}\right)&space;=$  $\par&space;Rs.&space;560$
$\par&space;C.P.&space;=&space;Rs.$ $\left(\frac{100}{112}\times&space;560\right)&space;=$  $\par&space;Rs.&space;500$			
20. Suneel bought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of Rs. 1100. How much did he spend on repairs if he made a profit of 20% ?

A. 620

B. 680

C. 720

D. 750

			$\par&space;Let&space;the&space;C.P.&space;be&space;Rs.&space;x.&space;Then,&space;20\%&space;of&space;x&space;=$ $\par&space;1100$
$\frac{20}{100}&space;\times&space;x$ $\par&space;=&space;1100$
$\par&space;x&space;=&space;5500$
$\par&space;C.P.&space;=&space;5500,$ $\par&space;Expenditures&space;on&space;repairs&space;=&space;10\%$
$\par&space;Actual&space;price&space;=&space;Rs.$ $\left(\frac{100}{110}\times&space;5500\right)&space;=$ $\par&space;Rs.&space;5000$
$\par&space;Expenditure&space;on&space;repairs&space;=&space;Rs.&space;(5500&space;-&space;5000)&space;=&space;Rs.&space;500$