Question : When a watch is sold at $\frac{7}{11}$ of the marked price, there is a loss of 20%. What is the ratio of the marked price to the cost price of this watch?
Option 1: 44 : 35
Option 2: 31 : 25
Option 3: 41 : 25
Option 4: 38 : 35
Correct Answer: 44 : 35
Solution :
Let the cost price be CP and the marked price as MP.
Given that when the watch is sold at $\frac{7}{11}$ of the MP, there is a loss of 20%.
This means that $\frac{7}{11}$ of the MP is 80% of the CP.
$⇒\frac{7}{11} \text{MP} = 0.8 \text{CP}$
Rearranging this equation to find the ratio of MP to CP,
$⇒\frac{\text{MP}}{\text{CP}} = \frac{0.8 \times 11}{7} = \frac{8.8}{7} = \frac{88}{70}=\frac{44}{35}$
Hence, the correct answer is 44 : 35.
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