Certainly! Let's solve this step-by-step.
Given:
- Selling price including 10% VAT = Rs. 26,180
- Discount rate = 15%
- Markup rate (above cost price) = 40%
Step-by-Step Solution:
(i) Find the Cost Price:
1. Calculate the price before VAT:
- The selling price includes a 10% VAT. To find the price before VAT, we remove the VAT component.
- Price before VAT = [tex]\( \frac{\text{Selling Price}}{1 + \text{VAT rate}} \)[/tex]
- Substituting the given values:
[tex]\[
\text{Price before VAT} = \frac{26180}{1 + 0.10} = \frac{26180}{1.10} = 23799.999999999996 \approx 23800
\][/tex]
2. Calculate the marked price:
- The price before VAT is inclusive of a 15% discount on the marked price. To find the marked price, we account for this discount.
- Marked Price = [tex]\( \frac{\text{Price before VAT}}{1 - \text{Discount rate}} \)[/tex]
- Substituting the values:
[tex]\[
\text{Marked Price} = \frac{23800}{1 - 0.15} = \frac{23800}{0.85} = 27999.999999999996 \approx 28000
\][/tex]
3. Calculate the cost price:
- The marked price is 40% above the cost price. To find the cost price, we account for the markup ratio.
- Cost Price = [tex]\( \frac{\text{Marked Price}}{1 + \text{Markup rate}} \)[/tex]
- Substituting the values:
[tex]\[
\text{Cost Price} = \frac{28000}{1 + 0.40} = \frac{28000}{1.40} = 20000
\][/tex]
(ii) Find the Marked Price:
- From the calculations above, the marked price is Rs. 28000.
(iii) Find the Profit Percentage:
1. Calculate the profit:
- Profit = Price before VAT - Cost Price
- Using previously calculated values:
[tex]\[
\text{Profit} = 23800 - 20000 = 3800
\][/tex]
2. Calculate the profit percentage:
- Profit Percentage = [tex]\( \frac{\text{Profit}}{\text{Cost Price}} \times 100 \)[/tex]
- Substituting the values:
[tex]\[
\text{Profit Percentage} = \frac{3800}{20000} \times 100 = 19\%
\][/tex]
Summary:
(i) The cost price is Rs. 20000.
(ii) The marked price is Rs. 28000.
(iii) The profit percentage is 19%.
