Profits And Loss Solved Problems

Profits And Loss Solved Problems


  • Posted by  Meghana 
    28 Jan, 2012

    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 ??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.

    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 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%??
    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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