### Problem 3: Finding the Selling Price
(a) Marked price = Rs 50000 and Discount = one-fifth of the marked price.
1. Calculate the discount:
[tex]\[
\text{Discount} = \frac{1}{5} \times \text{Marked Price} = \frac{1}{5} \times 50000 = 10000
\][/tex]
2. Subtract the discount from the marked price to find the selling price:
[tex]\[
\text{Selling Price} = \text{Marked Price} - \text{Discount} = 50000 - 10000 = 40000
\][/tex]
So, the selling price is Rs 40000.
(b) Marked price = Rs 80000 and Discount = one-eighth of the marked price.
1. Calculate the discount:
[tex]\[
\text{Discount} = \frac{1}{8} \times \text{Marked Price} = \frac{1}{8} \times 80000 = 10000
\][/tex]
2. Subtract the discount from the marked price to find the selling price:
[tex]\[
\text{Selling Price} = \text{Marked Price} - \text{Discount} = 80000 - 10000 = 70000
\][/tex]
So, the selling price is Rs 70000.
### Problem 4: Finding the Marked Price
(a) Selling price = Rs 4999.50 and Discount percentage = 10%.
1. Convert the discount percentage to a decimal:
[tex]\[
\text{Discount Percentage} = \frac{10}{100} = 0.10
\][/tex]
2. Since the selling price is 90% of the marked price (because 100% - 10% discount = 90%), we can express it as:
[tex]\[
\text{Selling Price} = \text{Marked Price} \times (1 - \text{Discount Percentage})
\][/tex]
Therefore:
[tex]\[
4999.50 = \text{Marked Price} \times 0.90
\][/tex]
3. Rearrange to solve for the marked price:
[tex]\[
\text{Marked Price} = \frac{4999.50}{0.90} = 5555
\][/tex]
So, the marked price is Rs 5555.
(b) Selling price = Rs 7110.40 and Discount percentage = 20%.
1. Convert the discount percentage to a decimal:
[tex]\[
\text{Discount Percentage} = \frac{20}{100} = 0.20
\][/tex]
2. Since the selling price is 80% of the marked price (because 100% - 20% discount = 80%), we can express it as:
[tex]\[
\text{Selling Price} = \text{Marked Price} \times (1 - \text{Discount Percentage})
\][/tex]
Therefore:
[tex]\[
7110.40 = \text{Marked Price} \times 0.80
\][/tex]
3. Rearrange to solve for the marked price:
[tex]\[
\text{Marked Price} = \frac{7110.40}{0.80} = 8888
\][/tex]
So, the marked price is Rs 8888.
