Answered

Discover the best answers to your questions with the help of IDNLearn.com. Discover in-depth answers from knowledgeable professionals, providing you with the information you need.

In the peak season of winter days, a retailer marked the price of an electric heater as Rs 4000 and 10% discount was given to make 20% profit. But in the summer days she increased the discount percent to get only 12% profit from the same type of heater. How much did she/he increase the discount percent?

Sagot :

Answer:

6%

Explanation:

The marked price of the electric heater = Rs 4000

• In winter, when 10% discount was given, the retailer made 20% profit.

• In summer, ,when the discount was increased by x%,, the retailer made 12% profit.

We want to find the value of x.

First, we find the sale price of the good after a 10% discount.

[tex]\begin{gathered} Sale\;Price=4000-(10\%\text{ of }4000) \\ =4000-400 \\ =\$3600 \end{gathered}[/tex]

Next, the retailer made a 20% profit when he sold the heater at $3600, we find the cost price of the heater.

[tex]\begin{gathered} \text{Percentage Profit}=\frac{\text{ Selling Price}-\text{ Cost Price}}{\text{ Cost Price}} \\ \frac{20}{100}=\frac{3600-CP}{CP} \\ 0.2=\frac{3600-CP}{CP} \\ \text{ Cross multiply} \\ 0.2CP=3600-CP \\ CP+0.2CP=3600 \\ 1.2CP=3600 \\ CP=\frac{3600}{1.2} \\ CP=3000 \end{gathered}[/tex]

The cost price of the water heater is Rs 3000.

In the summer, she increased the discount percent to get only 12% profit from the same type of heater.

We find the selling price that gives a 12% profit.

[tex]\begin{gathered} \text{Percentage Prof}\imaginaryI\text{t}=\frac{\text{Sell}\imaginaryI\text{ng Pr}\imaginaryI\text{ce}-\text{Cost Pr}\imaginaryI\text{ce}}{\text{Cost Pr}\imaginaryI\text{ce}} \\ \frac{12}{100}=\frac{SP-3000}{3000} \\ \frac{12}{100}\times3000=\frac{SP-3000}{3000}\times3000 \\ 360=SP-3000 \\ SP=3000+360 \\ SP=3,360 \end{gathered}[/tex]

The selling price in summer was $3,360.

Finally, we find the discount.

[tex]\begin{gathered} \frac{3360}{4000}=0.84 \\ \implies(1-0.84)\times4000=3360 \\ 0.16\times4000=3360 \end{gathered}[/tex]

The new discount was 16%.

Therefore:

[tex]x=16-10=6\%[/tex]

The retailer increased the discount by 6%.

We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thank you for visiting IDNLearn.com. We’re here to provide dependable answers, so visit us again soon.