Question

The marked price of an item is twice the cost price. For a gain of 15% what is the discount offered?​

Answer 1

Answer:

Let CP = Rs. 100

MP = Rs. 200

Gain = 15%

SP = 100 + 15% of 100 = Rs. 115

Discount = 200 - 115 = 85

% Discount = 85×100200

= 42.5%

Answer 2

Answer:

• For a gain of 15%, discount offered must be 42.5%.

Step-by-step explanation:

Given that:

• The marked price of an item is twice the cost price.

To Find:

• For a gain of 15%, what is the discount offered?

Let us assume:

• The cost price of the item be x.

Then,

• The marked price of the item will be 2x.

Calculating SP if, wanted a gain of 15%:

As we know that,

$\sf{SP=\dfrac{(100+gain\%)}{100}\times CP}$

Substituting the values,

$\rm{=\dfrac{(100+15)}{100}\times x}$

Solving further,

$\rm{=\dfrac{115}{100}\times x}$

Multiplying,

$\rm{=\dfrac{115x}{100}}$

Subtracting SP from marked price:

$\sf{\longmapsto2x-\dfrac{115x}{100}}$

Subtracting,

$\sf{\longmapsto\dfrac{200x-115x}{100}}$

$\sf{\longmapsto\dfrac{85x}{100}}$

Hence,

$\sf{Discount=Rs.\;\dfrac{85x}{100}}$

Finding discount percentage:

As we know that,

$\sf{Discount\%=\dfrac{Discount}{Marked\;Price}\times100}$

Substituting the values,

$\rm{\longmapsto\dfrac{85x}{100}\div2x\times100}$

$\rm{\longmapsto\dfrac{85x}{100}\times\dfrac{1}{2x}\times100}$

Cancelling,

$\rm{\longmapsto\dfrac{85\!\!\!\not{x}}{1\!\!\!\not{0}\!\!\!\not{0}}\times\dfrac{1}{2\!\!\!\not{x}}\times1\!\!\!\not{0}\!\!\!\not{0}}$

$\rm{\longmapsto\dfrac{85}{2}}$

Dividing the numbers,

$\rm{\longmapsto42.5}$

Hence,

• The required discount offered must be 42.5%.