Question : An item was sold at INR 5,474 after two successive discounts of 12.5% and 8% were offered on its Marked Price. What was the Marked Price (in INR) of the item?
Option 1: 6,750
Option 2: 7,000
Option 3: 6,800
Option 4: 6,600
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Correct Answer: 6,800
Solution :
Let the Marked Price of the item be $x$.
For a discount of 12.5%.
$\text{Discount}{_1}=12.5\%\text{ of }x=0.125x$
⇒ New price after first discount = $x$ - 0.125$x$ = 0.875$x$
For the Second discount = 8%
$\text{Discount}{_2}=8\%\text{ of }0.875x=0.07x$
⇒ New price after first discount = 0.875$x$ - 0.075$x$ = 0.805$x$
According to the question,
0.805$x$ = 5474
⇒ $x=\frac{5474}{0.805}$
⇒ $x$ = INR 6800
Hence, the correct answer is 6,800.
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