# Profit, Loss and Discount

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Profit Loss and Discount:

Basic Terms:

• Cost Price – The price at which any item is bought is known as the cost price of that item.
C.P. = 100 / (100 + Profit%) * S.P.
C.P. = 100 / (100 – Loss%) * S.P.

• Selling Price – The price at which any item is sold is known as the selling price of that item.
S.P. = (100 + Profit%)/100 * C.P.
S.P. = (100 – Loss%)/100 * C.P.

• Profit – If selling price of any item is more than the cost price of the item then there is a profit on the selling the item.

Profit = Selling Price – Cost Price

• Loss – If selling price of any item is less than the cost price of the item then there is a loss on the selling the item.

Loss = Cost Price – Selling Price

• Discount – Sometimes shopkeeper gives you some rebate on items on selling to their customers. This rebate is known as discount and discount is known as rebate.

Formulas:

• Percentage Profit =( Profit * 100 %) / CP
• Percentage Loss =( Loss * 100 %) / SP
• If there is a profit of x % on selling the item, then cost price of the item = SP * 100 / (100 + x) and selling price of the item = CP * (100 + x) / 100
• If there is a loss of x % on selling the item, then cost price of the item = SP * 100 / (100 – x) and selling price of the item = CP * (100 – x) / 100

# Aptitude Questions (Profit Loss and Discount):

1. When an item is sold for Rs. 34.80 and there is a loss of 2%. What is the cost price of the item?

A)    Rs. 26.10

B)    Rs. 43

C)    Rs. 43.20

D)    Rs. 46.40

E)    None of these

Explanation:

C.P. = Rs. (100/75*34.80) = Rs. 46.40

2. Ram buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, then what is his profit percent?

A)    32/7 %

B)    60/11%

C)    10%

D)    12%

E)    None of these

Explanation:

C.P. = Rs. (4700 + 800) = Rs. 5500
S.P. = Rs. 5800
Profit = S.P. – C.P. = 5800 – 5500 = 300
Profit% = (300/5500 * 100)% = 60/11%

3. The price of an item raised by 40% and then two successive discounts of 10% each are allowed. Ultimately the price of the item is:

A)    Increased by 10%

B)    Increased by 13.4%

C)    Decreased by 13%

D)    Decreased by 13.4%

E)    None of these

Explanation:

Let the price of an item = Rs. x
Then, new price of an item after 40% increase = Rs. 140x/100 = Rs. 14x/10
Price of an item after 10% discount = Rs. 14x/10 * 90/100 = Rs. 126x/100
Now, the price of an item after second 10%
Discount = Rs. 126x * 90 / 10000
= Rs. 1134x/1000
Net change = 1134x/1000 – x = 134x/1000
Percentage Change = ((134x/1000)/x)* 100% = 13.4%

4. A woman buys a cycle for Rs. 2400 and sells it at a loss of 25%. What is the selling price of the cycle?

A)    Rs. 1090

B)    Rs. 1160

C)    Rs. 1800

D)    Rs. 1202

E)    None of these

Explanation:

S.P. = 75% of Rs. 2400 = Rs. (75/100 * 2400) = Rs. 1800

5. If selling price of an item is 4/3 of its cost price, the profit in the transaction is:

A)    16(2/3)%

B)    20(1/2)%

C)    25(1/2 )%

D)    33(1/3 )1%

E)    None of these

Explanation:

Let C.P. = Rs. x. Then, S.P. = Rs. 4x/3, Profit = Rs. ((4x/3)- x) = Rs. x/3
∴ Profit% = (x/3* 1/x*100)%= 33(1/3 )%