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13 Nov 2023, 15:33
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B
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Difficulty:
95%
(hard)
Question Stats:
52% (02:09) correct
48%
(02:29)
wrong
based on 632
sessions
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A group of friends dined at a restaurant and paid a total of $132 for the food, beverages, tax, and tip. The tax was calculated as p% of the total price of the food and beverages. The tip was calculated as q% of the sum of the total price of the food and beverages and the tax. What was the amount of the tip?
(1) P = 10
(2) q = 20
(1) P = 10
(2) q = 20
13 Nov 2023, 23:06
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Arghi
- Cost of food = \(f\)
- Cost of beverages = \(b\)
- Tax = \((f+b)(\frac{p}{100})\)
- Food + Beverages + Tax = \((f+b)(1+\frac{p}{100})\)
- Tip= \((f+b)(1+\frac{p}{100})(\frac{q}{100})\)
- Food + Beverages + Tax + Tip= \((f+b)(1+\frac{p}{100})(1+\frac{q}{100}) = 135\)
Statement 1
(1) P = 10
\((f+b)(1+\frac{p}{100})(1+\frac{q}{100}) = 135\)
As we do not know the value of \(q\), we will not be able to find the value of the tip. Hence, the statement alone is not sufficient. We can eliminate A and D.
Statement 2
(2) q = 20
\((f+b)(1+\frac{p}{100})(1+\frac{q}{100}) = 135\)
\((f+b)(1+\frac{p}{100})(1+\frac{20}{100}) = 135\)
\((f+b)(1+\frac{p}{100})(\frac{6}{5}) = 135\)
\((f+b)(1+\frac{p}{100}) = 110\)
Tip = \((f+b)(1+\frac{p}{100})(\frac{q}{100})\)
= \(110*(\frac{20}{100})\)
= \(110*(\frac{1}{5}) = 22\)
The statement alone is sufficient.
Option B
05 Jul 2024, 05:36
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This is one of those questions that has many variabes and hence the way to solve it is ensuring that we draw inferences instead of solving these equations.
Watch this solution to see it in action.
Watch this solution to see it in action.
