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Profit and Loss

Cost Price : The price at which an article is purchased, is called as cost price, abbreviated as C.P.

Selling Price : The price at which an article is sold, is called its selling price, abbreviated as S.P.

Profit or Gain = (S.P.) - (C.P)

Loss = (C.P.) - (S.P.)

Loss or Gain is reckoned on C.P.

FORMULAE :

(i) Gain = (S.P.) - (C.P.) (ii) Gain% = {(Gain x100)/C.P}

(iii) Loss = (C.P.) - (S.P.) (iv) Loss% = {Loss x 100/ C.P}

(v) S.P. = { (100 + Gain%)/100} x C.P

(vi) S.P. ={ (100 - Loss%)/100} x C.P.

(vii) C.P.= { 100/(100 + Gain%)} x S.P.

(viii) C.P.= { 100/(100 - Loss%)} x S.P.

(ix) If an article is sold at a gain of 35% then S.P. = 135% of C.P.

(x) If an article is sold at a loss of 35%, then S.P. =65% of C.P.

SOLVED PROBLEMS

1. A man buys an article for Rs.27.50 and sells it for Rs. 28.60. Find his gain percent.

Sol. : C.P = Rs. 27.50, S.P. = Rs. 28.60

Gain = Rs. (28.60 - 27.50) = Rs. 1.10

Gain% = {(1.10/27.50) x 100 }% = 4%

2. If a radio is purchased for Rs.490 and sold for Rs. 465.50, find the loss per cent.

Sol : C.P. = Rs. 490, S.P. = Rs. 465.50

Loss = Rs. (490 - 465.50) = Rs. 24.50

Loss% = { (24.50 x 100)/490}% = 5%

3. By selling a book for Rs. 115.20, a man losses 10%. At what price should he sell it to gain 5% ?

Sol : Let the new S.P. be Rs. x

(100 - Loss%) : (1st S.P.) = (100 + Gain%) : (2nd S.P.)

or (100 - 10)/115.20 = (100 + 5)/x or x=134.40

New S.P. = Rs. 134.40

4. A trader Lost 20% by selling a watch for Rs. 1024. What percent shall he gain or lose by selling it for Rs. 1472 ?.

Sol : Let the gain be x% then,

80 : 1024 = (100 + x) : 1472 or 80/1024 = (100 + x)/1472

x= 15%

5. Ashok purchased a radio set and sold it to Shyam at a profit of 25% and Shyam sold it to Mohan at a loss of 10% and Mohan paid Rs. 675 for it. For how much did Ashok purchase it ?

Sol: Suppose Ashok purchased it for Rs. x

Then 90% of 125% of x =675

(90 x 125 x x)/(100 x 100) =675

x = 600

6. A man sold two houses for Rs. 675958 each. On one he gains 16% while on the other he loses 16%. How much does he gain or lose in the whole transaction ?

Sol : In such a question there is always loss. the selling price is immaterial.

Formula : Loss% = { ( Common Loss & Gain%)/10 }²

7. Hari purchased 25Kg of wheat at Rs. 4 per Kg and 35 Kg of wheat at Rs. 4.50 per Kg. He sold the mixture at Rs. 4.25 per Kg. Find his gain or loss.

Sol : Total C.P. = Rs. (25 x 4) + (35 x 4.50) = Rs. 257.50

Total S.P. = Rs (60 x 4.25) = Rs. 255

Loss = Rs. (257.50 -255) = Rs. 2.50

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

Sol : Let C.P. be Rs. x

1st S.P. = 125% of Rs. x = 125x/100 =5x/4

2nd C.P. = 80% of x +4x/5

2nd S.P. = 130% of 4x/5 = 6x/25

(5x/4) - (26x/25) = 10.50 or 21x/100 =10.50

x = Rs.50

9. A vendor bought a number of bananas at 6 for 5 rupees and sold at 4 for 3 rupees. Find his gain percent.

Sol : Suppose, number bought = LCM of 6,5,4,3 = 60

C.P. = Rs (5 x 60)/6 = Rs. 50

S.P. = Rs. (3 x60)/4 = Rs.45

Loss% = (5 x 100)/50% = 10%

10. 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 per cent

Sol : Formula { Error / (True value - Error) } x 100 %

Gain % = (40 x 100/ 960)% = 4 _1/6 %