PROFIT & LOSS

 PROFIT AND LOSS

Cost Price (C.P) - price at which an article is purchased. 

Selling Price (S.P) - price at which an article is sold.

1. If SP/CP > 1 - Gain or Profit (SP > CP)
2. If SP/CP < 1 - Loss (SP < CP) 

Loss or Gain is always based on C.P.

• If two items CP is equal & by selling x% gain on one and x% loss on other one. Then, overall no profit & no loss. 

• If two items SP is equal & by selling x% gain on one and x% loss on other one. Then, loss % is (x/10)².

■ If a trader professes to sell his goods at CP, but uses false weights, then 

Gain% = [error / (true value － error ) ✕ 100] %

■ Marked Price (MP) - price listed on the label 
■ Discount - the reduction offered on the list price, it may a value or percentage. 
■ Mark up - increment over the CP
■ SP after discount  of m% = MP (1 － m/100)
■ Margin = (SP － CP) / SP ✕ 100

• Discount - let buy X get Y

            Then, discount % = [Y / (X + Y)] × 100

• If m% & n% are two consecutive discounts on a sale,  then equivalent single discount = [(m + n) － mn/100] %

☆ Tricks of single equivalent discount - 

100 － [(100 － d₁)/100 × (100 － d₂)/100 × (100 － d₃)/100 ….. × 100]

☆ MP － discount % = CP + profit % = SP

Examples

1. A quintal of sugar is bought for Rs.500. Find SP per kg to gain 20%?
Solution:
          100 CP = 120 SP
    ⟹   500 CP = 600 SP
Then, SP per kg = 600/100 = 6/-

2. A person incurs 5% loss by selling a watch for Rs.1140. At what price should the watch be sold to earn 5% profit?
Solution:
        If 95 =  1140 SP
      then, 105 = 1140/95 × 105 = Rs.1260 new SP

3. A tradesman marks his goods at 25% above their CP & allows purchasers a discount of 25/2 % for cash. What profit does he make?

Solution:

       CP = 100,   MP = 125

       SP = 125 (1 − 25/2/100) = 109.4

      Profit  = 109.4 − 100 = 9.4

4. A tricycle is sold at a gain of 16%. Had it been sold for Rs.100 more, the gain would have been 20%. What is the cost price of the tricycle?

Solution:

  SP₁ = 116   SP₂ = 120

Difference of SP = 4

So, 4 SP difference = 100

Then, 100 SP = (100/4) × 100 = 2500 (Ans.)

      

Do it Yourself

1. A shopkeeper sells two articles at Rs.600 each, making a profit of 20% on the first article and a  loss of 20% on the second article. Find the net profit/loss that he makes.

A. 4% Loss 

B. 2% Loss

C. 1% Profit

D. No profit or loss

2. A fruit seller purchased 20 kg of apples at Rs.300. Out of total quantity, 2 kg of apples were rotten. At what price per kg he should sell the balance quantity of apples to get a profit of 20%?

A. Rs.36

B. Rs.20

C. Rs.18

D. Rs.15

3. A businessman gives 10% discount on the marked price of a watch. If the cost price of the watch is Rs.300, then find out the marked price to get a profit of 20%?

 A. Rs.300

B. Rs.360

C. Rs.400

D. Rs.450

4. Asim purchased rice of Rs.800. He sold 3/4 th out of purchased rice at a profit of 10% and rest part at a loss of 10%. Then find out the percentage of profit or loss in selling the total rice.

A. 2.5% Loss 

B. 5% Profit

C. 7.5% Profit

D. 10%  Loss

5. A seller marked a price of Rs.460 on a cycle and sold it giving 25% discount. If he got 15% profit, then find out the cost price purchased by him?

A. Rs.414

B. Rs.360

C. Rs.300

D. Rs.200

6. A man bought articles at 3 for Rs.2 & sold at 2 for Rs.3. The gain or loss percentage is :

A. 25% Loss

B. 100% Loss

C. 125% Gain

D. No gain, no loss

7. If cost price of 12 tables is equal to selling price of 16 tables. Find loss percentage?

A. 25%

B. 100%

C. 125%

D. No gain, no loss

8. If CP is 96% of SP, then what is profit percentage?

A. 25%

B. 25/6 %

C. 100%

D. None

Previous Years Questions 

1. If the CP of 24 eggs is equal to SP of 20 eggs, then what would be the percentage of gain or loss in the transaction? (Ans.)

2. A dealer allows 16% discount to the retailer on the printed price of an electrical appliance and still makes a profit of 5%. The retailer sales the same to the customer for Rs.540 at a discount of 10% on the printed price. What is the CP of the appliance for the dealer? (Ans.480)

3. Successive discounts of 20% and 10% are equivalent to a single discount of ________? (Ans.28%)

4. A man purchased an article for Rs.1500 and sold it at 25% above the CP. If he has to pay Rs.75 as tax on it,  his net profit percentage will be:_____

5. After allowing a discount of 20%, a radio is available for Rs.1200. Its marked price was : 

6. A merchant has 1000 kg sugar, part of which he sells at 8% profit and the rest at 18% profit.  He gains 14% on the whole.  The quantity sold at 8% profit is: 

7. A shopkeeper bought toffees at the rate of 10 for Rs. 15 and sold them at the rate of 16 for Rs. 40. Find his profit percentage. (correct to two decimal places). 

8. A man purchases a TV for Rs.8,000 and sells it at 10% loss. What is the selling price of TV?