At what percentage above the cost price must an article be marked so as to gain 20% after allowing a discount of 5%?

Answer

Hint: To solve this question we need to know the concept of marked price, cost price and discount. The first step is to make some assumptions and then solve the problem as per the condition given. Formula used to solve the question is $\text{SP = CP + Profit }\!\!\%\!\!\text{ }\!\!\times\!\!\text{ CP}$ and $\text{Marked Price = S}\text{.P - Discount}$ , here $\text{CP}$ and $\text{SP}$are cost price and selling price respectively.

Complete step by step solution:
To find the percentage above the cost price so that a customer gets a discount of $5\%$ and the shopkeeper has a profit of $33\%$ in an article he sells. To start with some assumptions that need to be taken. Let us consider the cost price of an article to be of rupees $100$ and the marked price of the object be rupees $x$. Writing it mathematically we get:
$\text{Cost Price}=100$
$\text{Marked Price}=x$
Since the cost price is $100$ and gain percent is $33\%$so the selling price become:
$\Rightarrow \text{C}\text{.P + 33 }\!\!\%\!\!\text{ }\!\!\times\!\!\text{ C}\text{.P}$
$\Rightarrow 100+33\%\times 100$
$\Rightarrow 100+\dfrac{33}{100}\times 100$
$\Rightarrow 100+33$
$\Rightarrow 133$
So the selling price of the article is rupees $133$.
The second part of the question is that the customer has a discount of $5\%$. On applying this condition we get:
$\Rightarrow x-5\%\times x=133$
$\Rightarrow x-\dfrac{5}{100}\times x=133$
$\Rightarrow \dfrac{95}{100}\times x=133$
$\Rightarrow x=\dfrac{133\times 100}{95}$
$\Rightarrow x=140$
Percentage above the cost price should the article be marked is:
$\Rightarrow \dfrac{\text{Marked price - Cost Price}}{\text{Cost Price}}\times 100$
$\Rightarrow \dfrac{140-100}{100}\times 100$
$\Rightarrow \dfrac{40}{100}\times 100$
$\Rightarrow 40\%$

$\therefore $ At $40\%$ percentage above the cost price must an article be marked so as to gain $33\%$ after allowing the customer a discount of $5\%$.

Note: Marked price is always expressed as the percentage of the cost price. Discount on a material is always applied on the marked price and not on the selling price or cost price. The difference between the marked price and the discount is selling price$\text{Marked price - Discount = Selling Price}$.

Multiple Choice Questions

161.

A basket contains 300 mangoes. 75 mangoes were distributed among some students. Find the percentage of mangoes left in the basket.

• 70%

• 72%

• 76%

• 75%

45 Views

162.At what percentage above the cost price must an article be marked so as to gain 33% after allowing a customer a discount of 5%?40%45%35%47%

A.

40%

Shortcut Method:

62 Views

163.

A man buys a table and chair for Rs. 500/-. He sells the table at a loss of 10% and chair at a gain of 10%. He still gains Rs. 10/- on the whole. The cost price of chair (in Rs) is:

• Rs. 200

• Rs. 250

• Rs. 300

• Rs. 350

C.

Rs. 300

Total cost  = Rs. 500
Total gain  = Rs. 10 which equals = 2% on Rs. 500 
Thus, Common percentage = 2%
Loss on table  = 10%
Gain on chair =  10%
By percentage rule:
Ratio of cost of table and chair is given by:
Table :  Chair
(10 - 2)%  : (2-(-10)% = 8 : 12  = 2 : 3
∴  Cost price of chair:
             

327 Views

164.

If the ratio of the cost price and the selling price of an article be 4 : 5, then the percentage of profit is 

• 

• 25%

• 15%

• 10%

B.

25%

Let the cost price of article  = 4x
           selling price of article  = 5x

40 Views

165.

A shopkeeper marks his goods 50% more than the cost price and allows a discount of 25%. His profit or loss percentage is:

• 37.5%

• 25.5%

• 12.5%

• 25%

C.

12.5%

Net percentage:

42 Views

166.

If the successive discounts be 20%, 10% and 5%, then the single equivalent rate of discount is

• 31.6%

• 31.5%

• 31%

• 31.4%

A.

31.6%

Single equivalent  = 

43 Views

167.

A man bought 25 creates of oranges for Rs 10,000/-. He lost 5 crates. In order to earn a total profit of 25% of the total cost, he would have to sell each of the remaining crates at:

• Rs 650/-

• Rs 625/-

• Rs 600/-

• Rs 575/-

B.

Rs 625/-

Purchased crates = 25
Lost crates = 5 
Net crates = (25 - 5) = 20 crates.
Let he sells remaining crates at Rs. x/-
Now, according to the question,

94 Views

168.

The selling price of 6 bananas is equal to the cost price of 8 bananas. Then the percentage of profit is

• 20%

• 

• 25%

• 30%

B.

Required Profit percentage:
 

40 Views

169.

A dealer marks his goods 20% above cost price. He then allows some discount on it and makes a profit of 8%. The rate of discount is

• 4%

• 6%

• 10%

• 12%

C.

10%

Shortcut Method:

69 Views

170.

A dealer allows a discount of 15%. A customer pays an amount of Rs 318.75 for an article. At what price is the article listed?

• Rs 366.50

• Rs 375.00

• Rs 350.00

• Rs 431.25

B.

Rs 375.00

Let the marked price of the article be Rs x
According to the question,

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