A man sell his type writer at 5% loss. If he sells it for Rs. 80 more, he gains 5%. The cost price of the typewriter is

Options

A. (a) 800
B. (b) 830
C. (c) 870
D. (d) 890

Answer

To solve the problem, we will denote the cost price of the typewriter as \( CP = X \).

1. **Selling Price at 5% Loss:**
When the man sells the typewriter at a 5% loss, the selling price (SP) can be calculated as:
\[ SP_1 = CP - (5\% \text{ of } CP) = X - 0.05X = 0.95X \]

2. **Selling Price at 5% Gain:**
If he sells it for Rs. 80 more, he gains 5%. The new selling price (SP) can be expressed as:
\[ SP_2 = CP + (5\% \text{ of } CP) = X + 0.05X = 1.05X \]

3. **Setting up the equation:**
According to the problem, the difference between the two selling prices is Rs. 80:
\[ SP_2 - SP_1 = 80 \]
Substituting the expressions for \( SP_1 \) and \( SP_2 \):
\[ 1.05X - 0.95X = 80 \]

4. **Simplifying the equation:**
\[ 0.10X = 80 \]

5. **Solving for \( X \):**
To find \( X \), divide both sides by 0.10:
\[ X = \frac{80}{0.10} = 800 \]

Thus, the cost price of the typewriter is Rs. 800.