Question

A bed is sold for Rs. 6400 at a loss of \(20\%\). What is the cost price (in Rupees)?

• A. 6000
• B. 3500
• C. 7000
• D. 8000

Hint:

For a loss of \(L\%\): \[ \boxed{\text{SP}=\text{CP}\times\frac{100-L}{100}} \] For a profit of \(P\%\): \[ \boxed{\text{SP}=\text{CP}\times\frac{100+P}{100}} \]

Answer 1

The Correct Option is D

Concept: When an article is sold at a loss, \[ \boxed{\text{Selling Price}=\text{Cost Price}\times\frac{100-\text{Loss}\%}{100}} \]

Step 1: Form the equation.
Given, \[ \text{Selling Price}=6400, \] and loss \[ =20\%. \] Hence, \[ 6400=\text{CP}\times\frac{80}{100}. \]

Step 2: Find the cost price.
\[ \text{CP} =6400\times\frac{100}{80} =6400\times\frac54 =8000. \]

Step 3: Verification.
Loss \[ =20\%\text{ of }8000 =1600. \] Selling price \[ =8000-1600=6400, \] which agrees with the given data.

Step 4: Final conclusion.
Therefore, the cost price of the bed is \[ \boxed{\text{Rs. }8000.} \]