Question : When a watch is sold at $\frac{7}{8}$ th of the marked price, there is a profit of 25%. At what percentage more than the cost price has the marked price of the watch been fixed? [Give your answer correct to 2 decimal places.]
Option 1: 34.46%
Option 2: 42.86%
Option 3: 37.15%
Option 4: 30%
Correct Answer: 42.86%
Solution :
Use :
Profit % = $\frac{\text{Profit}}{\text{Cost Price}}$×100
Let the Marked Price = $M$, Costb Price = $C$
According to the question
⇒ 25 = $\frac{\frac{7}{8}M - C}{C}$×100
⇒ $\frac{25}{100}$ = $\frac{7M - 8C}{8C}$
⇒ $\frac{1}{4}$ = $\frac{7M - 8C}{8C}$
⇒ $2C = 7M - 8C$
⇒ $10C = 7M$
⇒ $C = 0.7M$
Difference between the cost price and the marked price = $M - C = M - 0.7M = 0.3M$
⇒ percentage increase = $\frac{0.3M}{0.7M}$×100
= $\frac{300}{7}$×100
= 42.86%
Hence, the correct answer is 42.86%
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