Question

If the ratio between the cost price and marked price of an article is 2:3. If the selling price of that article is Rs 1920 and the shopkeeper gave two successive discounts of 20% on the marked price. Find the loss during this transaction?

Answer 1

Answer:

The loss during the transaction is found to be Rs. 80.

Step-by-step explanation:

We know that the shopkeeper has provided two succesive discounts of 20% on the marked price,

Let y be the marked price. Then, the selling price will be:

$SP=y-\frac{20}{100}y-(\frac{20}{100}(y-\frac{20}{100}y))$

Simplifying this, we can get:

$SP=y-0.2y-(0.2(y-0.2y))$

$SP=0.8y-(0.2(0.8y))$

$SP=0.8y-0.16y$

or we can say:

$SP=0.64y$

We are given the selling price as Rs.1920, so substituting this, we get:

$1920=0.64y$

or we can say:

$y=\frac{1920}{0.64}=3000$

Thus, the marked price is found to be Rs. 3000

Now, we are given the ratio between the cost price and marked price as 2:3,

We can represent this by letting cost price as $2x$ and the marked price as $3x$.

Equating $3x$ to the found marked price, we get:

$MP=3x=3000$

or we can say:

$x=1000$

By substituting $x$, we get the cost price as:

$CP=2\times1000=2000$

Thus, the cost price is found to be Rs. 2000

The loss during the transaction will be:

$loss= CP-SP$

$loss=2000-1920$

we get:

$loss=80$

So, there is a loss of Rs. 80 done during the transaction.

Answer 2

Concept introduction:

Ratio is a type of mathematical term which represents one upon another term which is unitless.

Given:

• Here it is given that  marked price of an article is $2:3$.
• selling price of that article is Rs $1920$
• shopkeeper gave two successive discounts of $20$‰.

To find:

We have to find the loss during this transaction.

Solution:

The loss during the transaction is found to be Rs. 80

We know that the shopkeeper has provided two succesive discounts of $20$% on the marked price,

Let y be the marked price. Then, the selling price will be:

$SP=y-0.2y-(0.2(y-0.2y))\\SP=0.8y-0.16y$

or we can say:

$SP=0.64y$

We are given the selling price as Rs.1920, so substituting this, we get:

$1920=0.64y$

or we can say:

$y=\frac{1920}{0.64} \\=3000$

Thus, the marked price is found to be Rs. $3000$

Now, we are given the ratio between the cost price and marked price as $2:3$

We can represent this by letting cost price as $2x$  and the marked price as $3x$

Equating  to the found marked price, we get:

$MP=3x=3000$

or we can say:

$x=1000$

By substituting , we get the cost price as:

$CP=2*1000\\=2000$

Thus, the cost price is found to be Rs. $2000$.

The loss during the transaction will be:

$CP-SP\\=2000-1920\\=80$

So, there is a loss of Rs. $80$ done during the transaction.