Question : A shopkeeper gives an additional concession of 5% on an item which is already discounted by 15% on the marked price. If the buyer pays INR 3,068.50 for the item, then find the marked price.
Option 1: INR 3,500
Option 2: INR 3,700
Option 3: INR 3,800
Option 4: INR 3,780
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Correct Answer: INR 3,800
Solution :
We know the formula for successive discounts,
Selling price = $MP(1 - \frac{D_1}{100})(1 - \frac{D_2}{100})$
Where $MP$ is the marked price and $D_1, D_2$ are the discounts.
$\mathrm{D_1=5}$%
$\mathrm{D_2=15}$%
On substituting the values,
$\mathrm{MP(1 - \frac{5}{100})(1 - \frac{15}{100})}=3068.50$
$⇒\mathrm{MP×( \frac{19}{20})×(\frac{17}{20})}=3068.50$
$⇒\mathrm{MP×( \frac{323}{400})}=3068.50$
$⇒\mathrm{MP}=\frac{400}{323}× 3068.50$
$⇒\mathrm{MP}=400×9.50$
$⇒\mathrm{MP}=3800$
Hence, the correct answer is INR 3,800.
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