## Profit and Loss Problems with Solutions

** PROFIT AND LOSS**

When a shopkeeper buys his goods from a manufacturer or a distributor, then seller sells goods with higher price to make ** profit**. Shopkeeper also gains some money by selling his goods to us. If he sells his goods at a lower price then he suffers

**Here are some common terms related to this topic.**

*loss.*: The price at which an article is purchased by a dealer.*COST PRICE (CP)*: The price at which an article is sold by a dealer.*SELLING PRICE (SP)*: If the selling price (SP) of an article is*PROFIT***more**than its cost price (CP), then the dealer makes a**profit**; (SP>CP).**Profit = SP-CP.**If the selling price of an article is*LOSS:***less than its cost price,**then the dealer suffers a**loss**; (CP>SP).**loss = CP-SP.**

Now we will find ;

**Profit percentage = {(profit X 100)/CP}%**

**Loss percentage = {(loss X 100)/CP}%**

Let’s discuss some problems on **profit and loss.**

*i)Rahima bought a bicycle for Rs1200 and sold it for Rs1104. Find her loss and loss percentage.*

*i)Rahima bought a bicycle for Rs1200 and sold it for Rs1104. Find her loss and loss percentage.*

**Solution: **We have

** **CP of bicycle = Rs1200

SP of bicycle = Rs1104

Loss = CP – SP = Rs (1200- 1104)

=Rs96

Loss percentage= {(96 X 100)/1200}%

=8%

Therefore, she had loss of Rs96 and her loss percentage is 8%.

*ii)A shopkeeper buys a showpiece at Rs150,and sells it at a profit of 12%. Find the selling price of the showpiece.*

*ii)A shopkeeper buys a showpiece at Rs150,and sells it at a profit of 12%. Find the selling price of the showpiece.*

**Solution: ** We have

CP of showpiece = Rs150

Profit percentage = 12%

Let the profit be **x**

According to the formula **profit percentage = {(profit X100)/CP}**

12/100= {(**x** X 100)/150}

Or 100**x = **(150 X 12)

** x ** = (150 X 12)/100

Or **x **= 3X6 = 18; profit is Rs18

So the selling price will be CP + PROFIT = 150 + 18 = 168

Therefore, the selling price of the showpiece will be Rs168.

*iii) Find the sellinfg price of a LCD tv which is purchased for Rs12400 and sold at a loss of 7%.*

*iii) Find the sellinfg price of a LCD tv which is purchased for Rs12400 and sold at a loss of 7%.*

**Solution: **We have

CP of LCD tv = Rs12400

Loss = 7% of CP

= 7/100 OF 12400 = Rs868

SP of LCD = CP – LOSS = Rs (12400 – 868) = Rs 11532

Therefore, selling price of LCDtv is Rs11532.

*iv) Selling price of a toy car is Rs540. If the shopkeeper got the profit of 20%, What is the cost price of this toy car?*

*iv) Selling price of a toy car is Rs540. If the shopkeeper got the profit of 20%, What is the cost price of this toy car?*

**Solution: ** We have

SP of toy car = Rs540

Profit = 20%

Let the CP of toy car be Rs**x, **then

**Profit = **20% of **x** = Rs(20X**x**)/100 = Rs **x** /5

SP of car = CP + Profit = Rs( **x **+**x**/5) = Rs 6**x**/5

According to the given condition , 6**x**/5= 540

Or, **x **= (540 X 5)/6 = Rs450

Therefore, cost price of the toy car is Rs450.

*v) A watch was sold for Rs532 at a loss of 5%, what was its cost price?*

*v) A watch was sold for Rs532 at a loss of 5%, what was its cost price?*

**Solution: **We have

SP of watch = Rs532

Loss = 5%

Let the CP of the watch be **x**

Loss = 5% of Rs**x** = 5**x**/100 = Rs **x**/20

SP pf the watch = CP – LOSS = Rs (**x **–**x**/20) = (20**x** –**x**)/20 = 19**x**/20

According to the question;

19**x**/20 = 532

Or , **x** = (532 X 20)/19

**x**= 28 X 20

Or, **x** = 560

Therefore, the cost price of the watch is Rs560.

*vi) Aditya purchased 120 reams of paper at Rs785 per ream. He spent Rs2800 on transaction, paid octroi at the rate of Rs10.50 per ream and paid Rs140 to the coolie. He then sold 45 reams at the rate of Rs864 per ream and 750 reams at the rate of Rs892 per ream. In whole transaction what is the profit or loss percent got by Aditya? *

*vi) Aditya purchased 120 reams of paper at Rs785 per ream. He spent Rs2800 on transaction, paid octroi at the rate of Rs10.50 per ream and paid Rs140 to the coolie. He then sold 45 reams at the rate of Rs864 per ream and 750 reams at the rate of Rs892 per ream. In whole transaction what is the profit or loss percent got by Aditya?*

** **

**Solution : **We have

CP of 1 ream = Rs785

CP of 120 reams = Rs( 785 X 120) = Rs94200

Cost of transaction = Rs2800

Payment to octroi = Rs (10.50 X 120) = Rs 1260

Money paid to coolie = Rs140

Total overhead expenses = Rs( 2800 + 1260 + 140) = Rs 4200

CP of 120 reams = actual CP + overhead expenses = Rs (94200+4200) = Rs98400

Total SP of 120 reams = Rs (864X45 + 892 X 75)

Rs( 38880 + 66900) = Rs 1,05,780

Here SP > CP

Gain = SP-CP

= Rs(105780 – 98400) = Rs7380

Gain % = (gain X 100)/CP = {(7380X 100)/98400] = (15/2)% = 7^{1}/_{2}%

Therefore, the profit percent in the whole transaction is 7^{1}/_{2}%.

*vii)Rana buys pencils at the rate of 10 pencils for Rs25 and sells them to Rony at 12 pencils for Rs37. Find gain or loss percent of Rana.*

*vii)Rana buys pencils at the rate of 10 pencils for Rs25 and sells them to Rony at 12 pencils for Rs37. Find gain or loss percent of Rana.*

* *

**Solution: **We have

CP of 10 pencils = Rs25

CP of 1 pencil = Rs25/10

SP of 12 pencils = Rs37

SP of 1 pencil = Rs 37/12

L.C.M. of 10 and 12 = 60

So, CP of 60 pencils = Rs {(25 X 60)/10} = Rs 150

SP of 60 pencils = Rs{(37 X 60)/12} = Rs185

As SP > CP so Rana has a profit;

Profit of Rana = Rs( 185 – 150) = Rs35

Profit% = (profit X 100)/CP = ( 35 X 100)/150 = 70/3% = 23^{1}/_{3} %

Therefore, Rana has 23^{1}/_{3} % profit by selling pencils to Rony.

*viii) The CP of 6 lemons is equal to the SP of 8 lemons. Find the loss percent.*

*viii) The CP of 6 lemons is equal to the SP of 8 lemons. Find the loss percent.*

**Solution: **We have,

** **Let CP of 6 lemons = SP of 8 lemons = Rs **x**

So, CP of lemons = Rs **x**

CP of 1 lemon = **x**/6

SP of 8 lemons = Rs**x**

SP of 1 lemon = Rs**x** /8

Loss = CP – SP = (**x**/6) – ( **x**/8) = ( 4-1) **x**/24 = 3**x**/24

Loss percent = (CP X 100)/ profit = {**x/**6X100} /**x** /24 = 25%

Therefore, the loss percent of lemon is 25%.

*ix) Prabhu bought a watch for his Rs960. What will be the sell price of the watch to get 5% profit?*

*ix) Prabhu bought a watch for his Rs960. What will be the sell price of the watch to get 5% profit?*

**Solution: ** We have

CP of the watch = Rs 960

Gain percent = 5%

So, Prabhu gains 5% of of CP = 5% of Rs960

= (5X960)/100 = Rs 48

SP = CP +GAIN

Rs (960 + 48) =+ Rs 1008

Therefore, Prabhu will sell the watch in Rs1008.

*x) Kamini bought a bicycle for Rs1650. She sold the bicycle at a loss of 8%, for how much did she sell it?*

*x) Kamini bought a bicycle for Rs1650. She sold the bicycle at a loss of 8%, for how much did she sell it?*

**Solution: **We have,

CP of the bicycle = Rs1650

LOSS = 8%

Loss= 8% of Rs1650 = (8 X1650)/100 = Rs132

SP = CP – LOSS = ( 1650 – 132) = Rs1518

Therefore, kamini had sold the bicycle at Rs1518.

*(Xi) Rehana sold a radio set for Rs1400 at a gain of 12% . For how much did she buy it?*

*(Xi) Rehana sold a radio set for Rs1400 at a gain of 12% . For how much did she buy it?*

**Solution: **we have

SP of radio set = Rs1400

GAIN % = 12%

Let the CP of radio set be Rs **x**

So gain = 12% of CP =( 12 X **x)**/ 100 =RS (3**x**)/25

SP =CP + GAIN

1400 = **x **+ 3** x**/25

**x + **3**x**/25 =1400

Or {(25**x**+3**x**)/25} = 1400

28**x = **1400 X 25

Or **x **= (1400 X 25)/28

Or **x **= 1250

Therefore, Rehana should buy the radio set at Rs1250.

*(Xii) Munna sold a chair for Rs 1800 at a loss of 6*^{1}/_{4}% .At what price did he purchase it ?

*(Xii) Munna sold a chair for Rs 1800 at a loss of 6*

^{1}/_{4}% .At what price did he purchase it ?* *

**Solution: **SP of the table = Rs1800

LOSS = 6^{1}/_{4}% = 25/4%

Let the CP be Rs **x**

Then, loss = 6^{1}/_{4}% of Rs **x **= Rs {(25 X **x**)/(4 X 100)}

Rs( **x**/16)

SP= CP – LOSS

1800 = **x **–** x**/16

**x**–** x **/16**= **1800

Or, (16**x **–** x**)/16 = 1800

15**x = ( **1800 X 16)

Or, **x **= (1800 X 16)/15 = 1920

Therefore, CP of the table is Rs1920.

*(xiii) A shopkeeper loses 10% by selling a table fan for Rs750 . what will be the sell price of the table fan to get profit of 5%.*

*(xiii) A shopkeeper loses 10% by selling a table fan for Rs750 . what will be the sell price of the table fan to get profit of 5%.*

* *

**Solution, **we know

SP of the table fan = Rs750

Loss = 10%

Let the CP be Rs **x.**

Loss= 10% of Rs **x **= Rs( 10 X **x**)/100

Rs **x**/10

SP = CP – LOSS

Or, 750 = **x **–** x**/10

**x**–** x**/10 = 750

Or, (10** x**–** x**)/ 10= 750

9**x**/10 = 750

Or, 9**x** = 750 X 10

**x **= (750 X 10)/9

Or, **x** = 2500/3

So, the CP is Rs(2500/3)

Gain required = 5%

According to the formula,

SP= {(100+Gain)/100}X CP

Or, SP= {(100+5)/100} X {2500/3}

Or, SP = Rs875.

Therefore, the shopkeeper must sell the table fan for Rs875.

*(xiv) A shopkeeper made marked price on washing machine Rs7500 and gave a discount of 6% on it. Find the selling price of the washing machine.*

* *

**Solution, **we have

Marked price(MP)= Rs 7500

Discount= 6%

Amount of discount = Rs( 6 X 7500)/100 = Rs450

SP= ( MP- discount)

= 7500-450

=7050.

Therefore, the selling price of the washing machine is Rs7050.

*(xv) An article which is marked at Rs975 is sold for Rs897. What percent discount is allowed?*

* *

**Solution,** we have

MP = Rs975

SP= Rs897

Discount = MP – SP = Rs( 975- 897) = Rs78

Rs975= Rs 78

Re 1= 78/975

Discount on Rs 100 = (78 X 100)/975 = 8%

Therefore, 8% discount is allowed in the article.

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