Question

Francis has 18 eggs out of which 12 eggs were sold at 10% loss than the cost price. At what mark up should he sell the remaining eggs to cover his losses?

• A. 5%
• B. 10%
• C. 15%
• D. 20%

Hint:

Use assumed CP = 1 to simplify profit/loss problems. When loss and gain are involved, equate total CP = total SP to find required markup.

Answer 1

The Correct Option is C

Let cost price of each egg = \( \rupee 1 \) (for simplicity).
Total cost of 18 eggs = \( 18 \times 1 = \rupee 18 \) Step 1: Loss on first 12 eggs
Sold at 10% loss, so selling price per egg = \( \rupee (1 - 0.10) = \rupee 0.90 \) \[ \text{Total SP for 12 eggs} = 12 \times 0.90 = \rupee 10.80 \] Step 2: Cost of remaining 6 eggs \[ \text{Cost} = 6 \times 1 = \rupee 6 \] Let the selling price of each of these 6 eggs be \( \rupee x \)
\[ \text{Total SP for 6 eggs} = 6x \] Step 3: Total SP of all eggs = Total Cost (no profit, no loss) \[ \text{Total SP} = \rupee 10.80 + 6x,\quad \text{Total Cost} = \rupee 18 \] \[ 10.80 + 6x = 18 \Rightarrow 6x = 7.2 \Rightarrow x = \frac{7.2}{6} = 1.20 \] So, SP per egg = \( \rupee 1.20 \), CP per egg = \( \rupee 1 \) \[ \text{Markup} = 1.20 - 1 = 0.20 = 20% \text{ gain on cost} \] Required Markup = 20% But wait! The options say (c) 15%. Let’s recheck. Alternative: Let markup be \( m% \). Then SP of each = \( 1 + \frac{m}{100} \) Total SP of 6 eggs = \( 6 \times \left(1 + \frac{m}{100} \right) \) \[ 10.80 + 6 \left(1 + \frac{m}{100} \right) = 18 \Rightarrow 10.80 + 6 + \frac{6m}{100} = 18 \] \[ 16.80 + \frac{6m}{100} = 18 \Rightarrow \frac{6m}{100} = 1.20 \Rightarrow m = \frac{1.20 \times 100}{6} = 20% \] Hence, correct answer is \( \boxed{20%} \) % Final Answer \[ \boxed{20%} \]