Question

A shopkeeper gives 3 consecutive discounts of 10%, 15% and 15% after which he sells his goods at a percentage profit of 30.05 percent on the cost price. Find the value of the percentage profit that the shopkeeper would have earned if he had given discounts of 10% and 15% only. ​

Answer 1

Hey Dear,

◆ Answer -

Profit % = 53 %

● Explaination -

Let x be the marked price and y be cost price of the goods.

Initially, he givez consecutive discounts of 10%, 15% and 15%.

After 10% discount,

Selling price = x - x × 10/100

Selling price = x - 0.1x

Selling price = 0.9x

After 1st 15% discount,

Selling price = 0.9x - 0.9x × 15/100

Selling price = 0.9x - 0.135x

Selling price = 0.765x

After next 15% discount,

Selling price = 0.765x - 0.765x × 15/100

Selling price = 0.765x - 0.11475x

Selling price = 0.65025x

Given that the shopkeeper earns 30.05 % profit at this selling price.

Profit % = Selling price / cost price - 1

30.05/100 = 0.65025x / y - 1

130.05/100 = 0.65025x / y

y = 65.025x / 130.05

y = 0.5x

We know that the selling price after 10% and 15% discount was 0.765x.

Profit % = Selling price / cost price - 1

Profit % = 0.765x / 0.5x - 1

Profit % = 1.53 - 1

Profit % = 0.53 = 0.53×100 %

Profit % = 53 %

Therefore, the shopkeeper would have earned 53% profit if he had given discounts of 10% and 15% only.

Best luck dear...

Answer 2

Answer:

The Answer is 53%

Step-by-step explanation:

Let The CP be 100

So Profit = 30.05%

Therefore SP = 130.05

MP = 130.05 x 100/90 x 100/85 x 100/85

So MP = 200

Now if Shopkeeper would have Given 10% and 15% Discount Respectively

SP = MP x (100-d1/100) x (100-d2/100)

So That = 200 x (100-10/100) x (100-15/100)

             = 200 x 90/100 x 85/100

       SP  = 153

So Profit = 53%