Aptitude Concept of Profit & Loss with Quiz

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.

 

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

 

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

 

2.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.

 

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

 

(m-n)/n×100%

 

4.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) 

 

 

5.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

 

6.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}%

 

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

 

(x +y - xy/100)%

 

8.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)% 

 

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

 

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

 

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

 

Some Important Concept

1. If a person sells two similar articles, one at a gain of a% and another at a loss of a%, then the seller always incurrs a loss which is given by
Loss%=(a/10)^2 %
2. If a'th part of some items is sold at x% loss, then required gain per cent in selling rest of the items in order that there is neither gain nor loss in whole transaction, is (ax)/(1-a)%
Example 1: A medical store owner purchased medicines worth Rs. 6000 form a company. He sold 1/3 part of the medicine at 30% loss. On which gain he should sell his rest of the medicines, so that he has neither gain or loss?

Here a = 1/3 , x = 30 % 
Required gain % = (1/3*30)/(1-1/3) = 15 % 
3. If cost price of 'a' articles is equal to the selling price of 'b' articles, then profit percentage 
=(a-b)*100/b
4. If a dishonest trader professes to sell his items at CP but uses false weight, then 

Gain %=Error*100/(True Value-Error)
Gain%=(True weight-False weight)/(False weight) X100%
Example 2: A dishonest dealer professes to sell his goods at cost price but he uses a weight of 930 g for 1 kg weight. Find his gain per cent.
Gain % = 70*100/930
5.If a shopkeeper sells his goods at a% loss on cost price but uses b g instead of c g, then his profit or loss is [(100-a)(c/b)-100]% as sign positive or negative
Example 3:A dealer sells goods at 6% loss on cost price but uses  14 g instead of 16 g. What is his percentage profit or loss?

Here a = 6 % , b = 14 g and c = 16 g

Required answer = [(100-6)(16/14)-100]% = 7(3/7) %
6. If a dealer sells his goods at a% profit on cost price and uses b% less weight, then his percentage profit  will be 
(b+a)/(100-b)X100%
Example 4: A dealer sells his goods at 20% loss on cost price but uses 40% less weight. What is his percentage profit  or loss?
Here a = 20 , b = 40 
Required answer = (40 -20)*100/(100- 40) = 33(1/3) %
7. If 'a' part of an article is sold at x% profit/loss, 'b' part at y% profit/loss and c part at z%  profit/loss and finally there is a profit/lossof Rs.R, then Cost price of entire article
=RS.(R*100)/(ax+by+cz) 
Example 5: If 2/3 part of an article is sold at 30% profit, 1/4 part at 16% profit and remaining part at 12% profit and finally, there is a profit of Rs.75, then find the cost price of the article.
Here a = 2/3 , x = 30 % , b =1/4 , y = 16 % , z = 12 % and R = 75 Rs
Required CP of article = (75*100)/(2/3*30+1/4*16+1/12*12)  = 7500/25 = 300


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

 

Solution - C

 

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. 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

 

Solution - B

 

Gain or loss = [2*5*4/4(5+4) - 1] × 100 % = 11.11% 

 

Sign is + ive so gain 11.11%
 

 

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

 

Solution - D

10 = x-5 – 5x/100

 

19x/20 = 15; x=15.789% = approx 15.8%

 

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

 

Solution - A

 

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. 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

 

Solution - D

 

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. 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

 

Solution - B

 

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. 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

 

Solution - C

 

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. 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

 

Solution - B

 

 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. 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.

 

Solution - C

 

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

 

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

 

Solution - C

 

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)