Question

A shop sells a watch for ₹B, incurring a loss of 8%. During a clearance sale, they mark it up to ₹1.3B. At the sale, they offer a discount of 15% on this marked price. What will be the percentage profit or loss during the sale?

• A. 3.8% profit
• B. 1.8% loss
• C. 1.6% profit
• D. 3.8% loss

Answer 1

Answer:

C. 1.6% profit

Let the cost price (CP) of the watch be (C).

Since selling it for ₹(B) results in an 8% loss,

$B = 92\% \text{ of } C = 0.92C.$

Hence,

$C=\frac{B}{0.92}.$

Find the sale price during the clearance sale

Marked price:

$=1.3B.$

Discount of 15%:

$\text{Sale Price} = 85$
$=0.85\times1.3B$
$=1.105B.$

Compare with the cost price

Using$(C=\dfrac{B}{0.92}),$

$\frac{\text{SP}}{\text{CP}}$
$=\frac{1.105B}{B/0.92}$
$=1.105\times0.92$
$=1.0166.$

Thus,

$\text{Profit \%}$
$=(1.0166-1)\times100$
$=1.66\%$.

More exactly,

$1.105\times0.92=\frac{221}{200}\times\frac{23}{25}$

$=\frac{5083}{5000}$

$=1.0166.$

So the profit percentage is

$\frac{83}{5000}\times100$
$=1.66\%.$