Question : On an item having a marked price of INR 1,600, successive discounts of $y$% and $z$% were offered. As a result, the item was sold for INR 1,056. Which of the options below CANNOT be a set of values for $y$ and $z$?
Option 1: $y=22, z=15.5$
Option 2: $y=4, z=31.25$
Option 3: $y=20, z=17.5$
Option 4: $y=12, z=25$
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Correct Answer: $y=22, z=15.5$
Solution :
Marked price = INR 1,600
Selling price = INR 1,056
Discount % = $\frac{\text{Discount}}{\text{Marked price}}\times 100$%
Discount % = $\frac{1600-1056}{1600}\times 100 =34\%$
Single discount $=y + z - \frac{yz}{100}$
Single discount of 22 and 15.5 $=22+15.5-\frac{22\times 15.5}{100}$
$=37.5-3.41 = 34.09\%$ which is not equal to $34\%$ and rest of the options satisfy the given condition.
Hence, the correct answer is $y=22,z=15.5$.
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