Concept of Profit & Loss with Quiz

Cost Price-The price at which an article is purchased is called its cost price (C.P.)

Selling Price-The price at which the article is sold is called its selling price (S.P.)

If the cost price (C.P.) of the article is equal to the selling price (S.P.), Then there is no loss or gain.

If the selling price (S.P.) > cost price (C.P.), then the seller is said to have a profit or gain,

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

If the cost price (C.P.) > selling price (S.P.), then the seller is said to have a loss,

Loss = C.P. - S.P.

Gain% = {Gain*100}/{C.P.}

Loss% = {Loss*100}/{C.P.}

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

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

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

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

If an article is sold at a profit/gain of 30%, then S.P. = 130% of the C.P.

If an article is sold at a loss of 20%, then S.P. = 80% of the C.P.

When there  are two successive Profit of x % and y % then the resultant profit  per cent is given by 

[x + y+ (x*y/100)]

If there is a Profit of  x% and loss of  y %  in a transaction, then the  resultant profit or loss% is given by 

[x – y - (x*y/100)]

Note-  For profit use sign + in previous formula and for loss use – sign.

if resultant come + then there will be overall profit . if it come – then  there will be overall loss.

If a cost price of m articles is equal to  the selling Price of n articles, then Profit percentage 

(m-n)/n×100%

If  m part is sold  at x% profit , n part is sold at y % profit, and p part is sold at z% profit and  Rs. R is earned as overall profit  then the value of total consignment 

R×100 / (mx+ny+pz) 

A man purchases a certain no. of article at m a rupee and the same no. at n a rupee. He mixes them together  and sold them at p a rupee then his gain or loss %

[{2mn/(m+n)p} -1]× 100

Note += profit ,- = loss

When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then in this transaction the seller always incurs a loss given by: = {x^2/100}%

A single discount equivalent to discount series of x% and y% given by the seller is equal to

(x +y - xy/100)%

If a seller marks his goods at x% above his cost price and allows purchasers a discount of y %  for cash,  then overall gain or loss 

(x – y –xy/100)% 

Profit or loss according to sign .+ = gain, - = loss

If a trader professes to sell his goods at cost price, but uses false weights, then 

Gain% = {(Error)/(True value - Error)x 100] %

Quiz Based on Concepts

1. 1/3 of a commodity is sold at 15% profit, ¼ is sold at 20% profit and the rest at 24% profit. If the Total profit is Rs. 80 is earned then find the value of commodity?

A) 350

B) 410

C) 400

D) 300
E) None of these

2. A man purchases a certain no. of apple at 5 per rupee and same no. at 4 per rupee. He mixes them together and sells them at 4 per rupee. What is  his gain or loss%?

A)  Gain 20 %

B)  Gain 11.11%

C) Loss 11.11%

D)  Loss 20 %
E) None of these

3. A trader allows a Discount of 5% for cash payment. How much approx % above cost price must he mark his goods to make a profit of 10%?

A) 8.9% 

B) 10%

C) 12.75%

D) 15.8%
E) None of these

4. If selling price is doubled, the profit triples. Find the profit percent?

A) 100%

B) 116.67%

C) 200%

D) 300%
E) None of these

5. The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?

A) 2200

B) 2400

C) 2500

D) 2000
E) None of these

6. Abhishek 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) 5.4

B) 5.6

C) 6.5

D) 4.5
E) None of these

7. Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:

A) 33.33%

B) 66.66%

C) 44%

D) 50%
E) None of these

8. On selling 17 toys at Rs. 720, there is a loss equal to the cost price of 5 toys . The cost price of a Toy is:

A) Rs. 50

B) Rs. 60 

C) Rs. 65

D) Rs. 70
E) None of these

9. A shopkeeper sells some articles at the profit of 25% on the original price. What is the exact amount of profit? To find the answer, which of the following information given in Statements I and II is/are Sufficent?

I. Sale price of the article

II. Number of articles sold

A)Only I is sufficient.

B)Only II is sufficient.

C)Both I & II are sufficient.

D)Either I or II are sufficient.

E)Both I & II are not sufficient.

10. A man purchases 10 Cows at Rs. 3000 each. 1 Cow died. He sold 2 Cows at 5% loss, at what rate he should sale the remaining Cows, so as to gain a Profit of 10 % on the total Cost?

A) Rs.4000

B) Rs.3000 

C) Rs.3900

D) Rs. 4500

E) Rs. 4200

Answers

1). C

2). B

3). D

4). A

5). D

6). B

7). C

8). B

9). C

10).C

Explanation:

1. Part sold at 24% profit = 1-(1/3+1/4) = 5/12
 Value of commodity = (80×100) / (1/3*15+1/4*20+5/12*24)= 400

2. Gain or loss = [2*5*4/4(5+4) - 1] × 100 % = 11.11% 
Sign is + ive so gain 11.11% 

3. 10 = x-5 – 5x/100
19x/20 = 15; x=15.789% = approx 15.8%

4. Let C.P. be Rs. x and S.P. be Rs. y.
Then, 3(y - x) = (2y - x)     y = 2x.
Profit = Rs. (y - x) = Rs. (2x - x) = Rs. x.
So profit % =100%

5. Let CP is x.
Then   (1920-x)/x*100= (x-1280)/x*100
On solving x=1600
Selling Price = 1600*125/100= Rs. 2000

6. Cost price of 1 Toy = 375/12= 31.25
Selling price of 1 toy = Rs.33
Profit= Rs (33-31.25) =1.75
Profit% = 1.75/31.25*100= 5.6

7. Lcm of 5&6 =30
Cost price of 30 articles= 5/6*30 = 25
Selling Price of 30 articles = 6/5*30 =36
% profit = (36-25)/25*100= 44% 

8. Cost price of 17 toys – Selling price of 17 toys = cost Price  of 5 toys
Cost price of 12 toys = selling Price of 17 toys= 720
Cost price of 1 toy= 720/12= 60 

9. Both I & II are sufficient to find the exact amount of profit .

10. Selling Price With Profit of 10 %  of total cost = 3000*10*110/100= 33000
Selling Price of 2 cows with 5% loss= 6000*95/100= 5700
Difference = 33000-5700= 27300;
So rate of the cows for selling to gain 10% profit on total = 27300/7= Rs. 3900
(because 1 cow died so remaining= 10-1-2=7)