ex.1 A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain %. sol. cp=rs27.50, sp=rs 28.50 gain=rs(28.50 â??27.50)=rs1.10 so gain%={(1.10/27.50)*100}=4%

ex.2. If the a radio Cost Price is rs 490 and sold for rs 465.50.find loss%. sol. cp=rs490,sp= 465.50. loss=rs(490-465.50)=rs 24.50. loss%=[(24.50/490)*100]%=5%

ex.3.find S.P when (i)CP=56.25,gain=20%. sol. (i)SP =20% of rs 56.25 ,=rs{(120/100)*56.25}=rs67.50.

(ii)CP=rs 80.40,loss=5% sol: sp=85% of rs 80.40 =rs {(85/100)*80.40}=rs 68.34.

(i) cp=rs{(100/116)*40.60}=rs 35. (ii) cp=rs{(100/88)*51.87}=rs58.75.

ex.5 A person incures loss for by selling a watch for rs1140.at what price should the watch be sold to earn a 5% profit ?

sol. let the new sp be rsx.then =>(100-loss%) : (1st sp)=(100+gain%) (2nd sp) =>{(100-5)/1400}={(100+5)/x}=> x={(105*1140)/95} =1260.

ex.6 A book was sold for rs 27.50 with a profit of 10%. if it were sold for rs25.75, then what would be % of profit or loss?sol. SP=rs 27.50: profit =10%. sol. CP=rs {(100/110)*27.50}=rs 25. When sp =Rs25.75 ,profit =Rs(25.75-25)=Rs 0.75 Profit%={(0.75/25)*100}%=25/6%=3%

ex7 .If the cost price is 96% of sp then whqt is the profit % sol. sp=Rs100 : then cp=Rs 96:profit =Rs 4. Profit={(4/96)*100}%=4.17% ex.8. The cp of 21 articles is equal to sp of 18 articles.find gain or loss % sol:CP of each article be Rs 1 CP of 18 articles =Rs18 ,sp of 18 articles =Rs 21. Gain%=[(3/18)*100]%=50/3%

ex.9 By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent . sol: (SP of 33m)-(CP of 33m)=Gain=SP of 11m SP of 22m = CP of 33m Let CP of each metre be Re.1 , Then, CP of 22m= Rs.22,SP of 22m=Rs.33. Gain%=[(11/22)*100]%=50%

ex10 A vendor bought bananas at 6 for Rs.10 and sold them at Rs.4 for Rs.6 .Find his gain or loss percent . sol: Suppose , number of bananas bought = LCM of 6 and 4=12 CP=Rs.[(10/6)*12]=Rs.20 ; SP= Rs[(6/4)*12]=Rs.18 Loss%=[(2/20)*100]%=10%

ex.11. A man brought toffees at for a rupee. How many for a rupee must he sell to gain 50%? sol. C.P of 3 toffees=Re 1; S.P of 3 toffees =150% of Re.1=3/2. For Rs.3/2, toffees sold =3, for Re.1, toffees sold = [3*(2/3)] = 2.

ex. 12.A grocer purchased 80 kg of sugar at Rs.13.50 per kg and mixed it with 120kg sugar at Rs.16per kg. At what rate should he sell the mixer to gain 16%? sol .C.P of 200 kg of mixture = Rs. (80 * 13.50+120*16) = Rs.3000. S.P =116% 0f Rs.3000 =Rs.[(116/200) *3000]=Rs.3480. =>Rate of S.P of the mixture =Rs.[3480/200] per kg =Rs.17.40 per kg.

ex. 14. A dishonest dealer professes to sell his goods at cost price but uses a weight of 960 gms for a kg weight . Find his gain percent. sol .Gain% =[(Error/(error value)-(error) )*100]% = [(40/960)*100] % = 4 1/6 %

ex 15. If the manufacturer gains 10%,the wholesale dealer 15% and the retailer 25%,then find the cost of production of a ,the retail price of which is Rs.1265?

sol: Let the cost of production of the table be Rs x The ,125% of 115% of 110% of x=1265 =>125/100*115/100*110/100*x=1265=>253/160*x=>1265=>x=(1265*160/253)=Rs.800 ex16 . Monika purchesed a pressure cooker at 9/10th of its selling price and sold it at 8% more than its S.P .find her gain percent.

sol: Let the s.p be Rs. X .then C.P = Rs.9x/10,Receipt=108% of rs.x=Rs 27x/25 Gain=Rs (27x/25*9x/10)=Rs(108x-90x/100)=Rs18x/100 Gain%=(18x/100*10/9x*100)%=20%

ex .17 An article is sold at certain price. By selling it at 2/3 of its price one losses 10%,find the gain at original price ?

sol: let the original s.p be Rs x. then now S.P=Rs2x/3,loss=10% now C.P=Rs20x/27*27/20x*100)%=35% ex .18. A tradesman sold an article at a loss of 20%.if the selling price has been increased by Rs100,ther would have been a gain of 5%.what was the cost price of the article? sol: Let C.P be Rs x. then (105% of x)-(80 % of x)=100 or 25% of x=100 =>x/4=100 or x=400 =>so,C.P =Rs 400 ex 19. A man sells an article at a profit of 25%if he had bought it 20% less and sold it for Rs 10.50 less,he would have gained 30%find the cost price of the article. sol: Let the C.P be Rs x 1st S.P=125% of x =125x/100=5x/4;2nd S.P=80% of x=80x/100=4x/5 2nd S.P=130% of 4x/5=(130/100*4x/5)=26x/25 =>5x/4-26x/25=10.50=>x=(10.50*100)/21=50 hence C.P=Rs.50 ex 20.The price of the jewel,passing through three hands,rises on the whole by65%.if the first and the second sellers 20%and25% profit respectively find the percentage profit earned by the third seller. sol: Let the orginal price of the jewel be Rs p and let the profit earned by the thrid seller be x% Then,(100+x)% of 125% OF 120% OF P=165% OF P =>((100+X)/100*125/100*120/100*P)=(165/100*P) =>(100+X)=(165*100*100)/(125*120)=110=>X=10% ex21 . A man 2 flats for Rs 675958 each.on one he gains 16% while on the other he losses 16%. How much does he gain/loss in the whole transaction? sol: In this case there will be alwalys loss. The selling price is immaterial Hence, loss % = (common loss and gain%)2 /10=(16/10)%=(64/25)%=2.56% ex.22. A dealer sold three-fourth of his article at a gain of 20% and remaining at a cost price. Find the gain earned by him at the two transcation. sol: Let the C.P of the whole be Rs x C.P of 3/4th =Rs 3x/4,C.P of 1/4th =Rs x/4 =>total S.P=Rs [(120%of 3x/4)+x/4]=Rs(9x/10+x/4)=Rs 23x/20 =>gain=Rs(23x/20-x)=Rs 3x/20 =>gain%=3x/20*1/x*100)%=15% ex 23 ..A man bought a horse and a car riage for Rs 3000.he sold the horse at a gain of 20% and the carriage at a loss of 10%,thereby gaining 2% on the whole.find the cost of the horse. sol: Let the C.p of the horse be Rs.x, then C.P of the carriage =Rs(3000-x) 20% of x-10% of(3000-x)=2% of 3000 =>x/5-(3000-x)/10=60=.2x-3000+x=600=.3x+3600=>x=1200 =>hence,C.P of the horse =Rs 1200 ex 24 find the single discount equivalent to a series discount of 20% ,10% and 5%â?? sol: let the marked price be Rs 100 then ,net S.P=95% of 90% of 80% of Rs 100 =Rs(95/100*90/100*80/100*100)=Rs68.40 ex .25 After getting 2 successive discounts, a shirt with a list price of Rs 150 is available at Rs 105. If the second discount is 12.55,find the first discount. sol: Let the first discount be x% Then,87.5% of (100-x)% of 150= 105 =>87.5/100*(100-x)/100*450=150=>105=>100-x=(105*100*100)/(150*87.5)=80 =>x=(100-80)=20 =>first discount = 20% ex .26 An uneducated retailar marks all its goods at 50% above the cost price and thinking that he will still make 25% profit,offers a discount of 25% on the marked price.what is the actual profit on the sales? sol: Let C.P =Rs 100.then ,marked price =Rs100 S.P=75% of Rs 150=Rs112.50 Hence,gain%=12.50% ex27 .A retailer buys 40 pens at the market price of 36 pens from a wholesaler ,if he sells these pens giving a discount of 1% ,what is the profit % ? sol: let the market price of each pen be Rs 1 then,C.P of 40 pens = Rs 36 S.P of 40 pens =99% of Rs 40=Rs 39.60 profit %=((3.60*100)/36) %=10% ex 28 . At what % above C.P must an article be marked so as to gain 33% after allowing a customer a discount of 5%? sol Let C.P be Rs 100.then S.P be Rs 133 Let the market price be Rs x Then 90% of x=133=>95x/100=133=>x=(133*100/95)=140 Market price = 40% above C.P ex .29 . When a producer allows 36% commission on retail price of his product, he earns a profit of 8.8%. what would be his profit % if the commision is reduced by 24%? sol: Let the retail price =Rs 100.then, commission=Rs 36 S.P=Rs(100-36)=Rs 64 But, profit=8.8% C.P=Rs(100/108.8*64)=Rs 1000/17 New commission =Rs12. New S.P=Rs(100-12)Rs 88 Gain=Rs(88-1000/17)=Rs 496/17 Gain%=(496/17*17/1000*100)%=49.6%

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ex.1 A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain %.

sol. cp=rs27.50, sp=rs 28.50gain=rs(28.50 â??27.50)=rs1.10

so gain%={(1.10/27.50)*100}=4%

ex.2. If the a radio Cost Price is rs 490 and sold for rs 465.50.find loss%.

sol. cp=rs490,sp= 465.50.loss=rs(490-465.50)=rs 24.50.

loss%=[(24.50/490)*100]%=5%

ex.3.find S.P when

sol.(i)CP=56.25,gain=20%.

(i)SP =20% of rs 56.25 ,=rs{(120/100)*56.25}=rs67.50.

(ii)CP=rs 80.40,loss=5%

sol: sp=85% of rs 80.40

=rs {(85/100)*80.40}=rs 68.34.

ex.4 find cp when:(i) sp =rs 40.60 : gain=16%

(ii) sp=rs51.70:loss=12%

(i) cp=rs{(100/116)*40.60}=rs 35.

(ii) cp=rs{(100/88)*51.87}=rs58.75.

ex.5 A person incures loss for by selling a watch for rs1140.at what price should the watch be sold to earn a 5% profit ?

sol. let the new sp be rsx.then=>(100-loss%) : (1st sp)=(100+gain%) (2nd sp)

=>{(100-5)/1400}={(100+5)/x}=> x={(105*1140)/95} =1260.

ex.6 A book was sold for rs 27.50 with a profit of 10%. if it were sold for rs25.75, then what would be % of profit or loss?sol. SP=rs 27.50: profit =10%.

sol. CP=rs {(100/110)*27.50}=rs 25.When sp =Rs25.75 ,profit =Rs(25.75-25)=Rs 0.75

Profit%={(0.75/25)*100}%=25/6%=3%

ex7 .If the cost price is 96% of sp then whqt is the profit %

sol. sp=Rs100 : then cp=Rs 96:profit =Rs 4.Profit={(4/96)*100}%=4.17%

ex.8. The cp of 21 articles is equal to sp of 18 articles.find gain or loss %

sol:CP of each article be Rs 1CP of 18 articles =Rs18 ,sp of 18 articles =Rs 21.

Gain%=[(3/18)*100]%=50/3%

ex.9 By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent .

sol:(SP of 33m)-(CP of 33m)=Gain=SP of 11m

SP of 22m = CP of 33m

Let CP of each metre be Re.1 , Then, CP of 22m= Rs.22,SP of 22m=Rs.33.

Gain%=[(11/22)*100]%=50%

ex10 A vendor bought bananas at 6 for Rs.10 and sold them at Rs.4 for Rs.6 .Find his gain or loss percent .

sol:Suppose , number of bananas bought = LCM of 6 and 4=12

CP=Rs.[(10/6)*12]=Rs.20 ; SP= Rs[(6/4)*12]=Rs.18

Loss%=[(2/20)*100]%=10%

ex.11. A man brought toffees at for a rupee. How many for a rupee must he sell to gain 50%?

sol. C.P of 3 toffees=Re 1; S.P of 3 toffees =150% of Re.1=3/2.For Rs.3/2, toffees sold =3, for Re.1, toffees sold = [3*(2/3)] = 2.

ex. 12.A grocer purchased 80 kg of sugar at Rs.13.50 per kg and mixed it with 120kg sugar at Rs.16per kg. At what rate should he sell the mixer to gain 16%?

sol .C.P of 200 kg of mixture = Rs. (80 * 13.50+120*16) = Rs.3000.S.P =116% 0f Rs.3000 =Rs.[(116/200) *3000]=Rs.3480.

=>Rate of S.P of the mixture =Rs.[3480/200] per kg =Rs.17.40 per kg.

ex. 14. A dishonest dealer professes to sell his goods at cost price but uses a weight of 960 gms for a kg weight . Find his gain percent.

sol .Gain% =[(Error/(error value)-(error) )*100]% = [(40/960)*100] % = 4 1/6 %ex 15. If the manufacturer gains 10%,the wholesale dealer 15% and the retailer 25%,then find the cost of production of a ,the retail price of which is Rs.1265?

sol:Let the cost of production of the table be Rs x

The ,125% of 115% of 110% of x=1265

=>125/100*115/100*110/100*x=1265=>253/160*x=>1265=>x=(1265*160/253)=Rs.800

ex16 . Monika purchesed a pressure cooker at 9/10th of its selling price and sold it at 8% more than its S.P .find her gain percent.

sol:Let the s.p be Rs. X .then C.P = Rs.9x/10,Receipt=108% of rs.x=Rs 27x/25

Gain=Rs (27x/25*9x/10)=Rs(108x-90x/100)=Rs18x/100

Gain%=(18x/100*10/9x*100)%=20%

ex .17 An article is sold at certain price. By selling it at 2/3 of its price one losses 10%,find the gain at original price ?

sol:let the original s.p be Rs x. then now S.P=Rs2x/3,loss=10%

now C.P=Rs20x/27*27/20x*100)%=35%

ex .18. A tradesman sold an article at a loss of 20%.if the selling price has been increased by Rs100,ther would have been a gain of 5%.what was the cost price of the article?

sol:Let C.P be Rs x. then (105% of x)-(80 % of x)=100 or 25% of x=100

=>x/4=100 or x=400

=>so,C.P =Rs 400

ex 19. A man sells an article at a profit of 25%if he had bought it 20% less and sold it for Rs 10.50 less,he would have gained 30%find the cost price of the article.

sol:Let the C.P be Rs x

1st S.P=125% of x =125x/100=5x/4;2nd S.P=80% of x=80x/100=4x/5

2nd S.P=130% of 4x/5=(130/100*4x/5)=26x/25

=>5x/4-26x/25=10.50=>x=(10.50*100)/21=50

hence C.P=Rs.50

ex 20.The price of the jewel,passing through three hands,rises on the whole by65%.if the first and the second sellers 20%and25% profit respectively find the percentage profit earned by the third seller.

sol:Let the orginal price of the jewel be Rs p and let the profit earned by the thrid seller be x%

Then,(100+x)% of 125% OF 120% OF P=165% OF P

=>((100+X)/100*125/100*120/100*P)=(165/100*P)

=>(100+X)=(165*100*100)/(125*120)=110=>X=10%

ex21 . A man 2 flats for Rs 675958 each.on one he gains 16% while on the other he losses 16%. How much does he gain/loss in the whole transaction?

sol:In this case there will be alwalys loss. The selling price is immaterial

Hence, loss % = (common loss and gain%)2 /10=(16/10)%=(64/25)%=2.56%

ex.22. A dealer sold three-fourth of his article at a gain of 20% and remaining at a cost price. Find the gain earned by him at the two transcation.

sol:Let the C.P of the whole be Rs x

C.P of 3/4th =Rs 3x/4,C.P of 1/4th =Rs x/4

=>total S.P=Rs [(120%of 3x/4)+x/4]=Rs(9x/10+x/4)=Rs 23x/20

=>gain=Rs(23x/20-x)=Rs 3x/20

=>gain%=3x/20*1/x*100)%=15%

ex 23 ..A man bought a horse and a car riage for Rs 3000.he sold the horse at a gain of 20% and the carriage at a loss of 10%,thereby gaining 2% on the whole.find the cost of the horse.

sol:Let the C.p of the horse be Rs.x, then C.P of the carriage =Rs(3000-x)

20% of x-10% of(3000-x)=2% of 3000

=>x/5-(3000-x)/10=60=.2x-3000+x=600=.3x+3600=>x=1200

=>hence,C.P of the horse =Rs 1200

ex 24 find the single discount equivalent to a series discount of 20% ,10% and 5%â??

sol:let the marked price be Rs 100

then ,net S.P=95% of 90% of 80% of Rs 100

=Rs(95/100*90/100*80/100*100)=Rs68.40

ex .25 After getting 2 successive discounts, a shirt with a list price of Rs 150 is available at Rs 105. If the second discount is 12.55,find the first discount.

sol:Let the first discount be x%

Then,87.5% of (100-x)% of 150= 105

=>87.5/100*(100-x)/100*450=150=>105=>100-x=(105*100*100)/(150*87.5)=80

=>x=(100-80)=20

=>first discount = 20%

ex .26 An uneducated retailar marks all its goods at 50% above the cost price and thinking that he will still make 25% profit,offers a discount of 25% on the marked price.what is the actual profit on the sales?

sol:Let C.P =Rs 100.then ,marked price =Rs100

S.P=75% of Rs 150=Rs112.50

Hence,gain%=12.50%

ex27 .A retailer buys 40 pens at the market price of 36 pens from a wholesaler ,if he sells these pens giving a discount of 1% ,what is the profit % ?

sol:let the market price of each pen be Rs 1

then,C.P of 40 pens = Rs 36 S.P of 40 pens =99% of Rs 40=Rs 39.60

profit %=((3.60*100)/36) %=10%

ex 28 . At what % above C.P must an article be marked so as to gain 33% after allowing a customer a discount of 5%?

solLet C.P be Rs 100.then S.P be Rs 133

Let the market price be Rs x

Then 90% of x=133=>95x/100=133=>x=(133*100/95)=140

Market price = 40% above C.P

ex .29 . When a producer allows 36% commission on retail price of his product, he earns a profit of 8.8%. what would be his profit % if the commision is reduced by 24%?

sol:Let the retail price =Rs 100.then, commission=Rs 36

S.P=Rs(100-36)=Rs 64

But, profit=8.8%

C.P=Rs(100/108.8*64)=Rs 1000/17

New commission =Rs12. New S.P=Rs(100-12)Rs 88

Gain=Rs(88-1000/17)=Rs 496/17

Gain%=(496/17*17/1000*100)%=49.6%