Question : The marked price of a washing machine is INR 7,200. If it is sold for INR 5,512.50, after two successive discounts of $x$% each. The value of $x$ is:
Option 1: 12
Option 2: 12.5
Option 3: 10.5
Option 4: 15
Correct Answer: 12.5
Solution :
Marked price, MP = INR 7,200
Selling price, SP = INR 5,512.50
Let $x$ be the discount(D).
For two successive discounts, The selling price = marked price × $\frac{100-\text{Discount}_1\%}{100}× \frac{100-\text{Discount}_2\%}{100}$
⇒ $5512.50 = 7200 ×\frac{(100 - x)}{100}×\frac{(100 - x)}{100}$
⇒ $[\frac{(100 - x)}{100} ]^2= \frac{5512.50}{7200}$
⇒ $[\frac{(100 - x)}{100}]^2 = \frac{49}{64}$
⇒ $\frac{(100 - x)}{100} = \frac{7}{8}$
⇒ $800-8x = 700$
⇒ $8x = 100$
⇒ $x = 12.5$
Hence, the correct answer is 12.5.
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