### Detailed Step-by-Step Solution:
Ramlal went to a shop to buy a gas stove. He bought the gas stove at a 10% discount on the marked price of Rs. 4200.
#### (a) छुट प्रतिशत निकाल्ने सूत्र लेखनुहोस् । Write the formula to find discount percent.
The formula to calculate the discount percent is:
[tex]\[ \text{Discount Percent} = \left( \frac{\text{Discount}}{\text{Marked Price}} \right) \times 100 \% \][/tex]
#### (b) उनले उक्त चुलो किन्दा कति छुट पाएछन् ? How much discount did he get while buying the stove?
Given:
- Marked Price (MP) = Rs. 4200
- Discount Percent = 10%
To find the discount amount, use the formula:
[tex]\[ \text{Discount} = \frac{\text{Discount Percent}}{100} \times \text{Marked Price} \][/tex]
Substituting the given values:
[tex]\[ \text{Discount} = \frac{10}{100} \times 4200 \][/tex]
[tex]\[ \text{Discount} = 0.1 \times 4200 \][/tex]
[tex]\[ \text{Discount} = 420 \][/tex]
So, the discount he got is Rs. 420.
#### (c) उक्त चुलो बेच्दा पसलेलाई [tex]$5.5 \%$[/tex] नोक्सान भएको रहेछ भने उक्त चुलोको क्रय मूल्य पत्ता लगाउनुहोस् । While selling that stove the shopkeeper had [tex]$5.5 \%$[/tex] loss, find the cost price of the stove.
Given:
- Loss Percent = 5.5%
- The selling price (SP) after discount can be calculated as:
[tex]\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} \][/tex]
Given the values:
[tex]\[ \text{Selling Price} = 4200 - 420 \][/tex]
[tex]\[ \text{Selling Price} = 3780 \][/tex]
Now, we need to find the Cost Price (CP). Using the relationship between the cost price, selling price, and loss percent:
[tex]\[ \text{Cost Price} = \frac{\text{Selling Price}}{1 - \left(\frac{\text{Loss Percent}}{100}\right)} \][/tex]
Substituting the given values:
[tex]\[ \text{Cost Price} = \frac{3780}{1 - \frac{5.5}{100}} \][/tex]
[tex]\[ \text{Cost Price} = \frac{3780}{1 - 0.055} \][/tex]
[tex]\[ \text{Cost Price} = \frac{3780}{0.945} \][/tex]
[tex]\[ \text{Cost Price} \approx 4000 \][/tex]
So, the cost price of the stove is Rs. 4000.
