A waiter's salary consists of his salary and tips. During one week his tips were $\frac{5}{4}$ of his salary. What fraction of his income came from tips?
Aptitude
Simplification
Difficulty: Easy
Choose an option
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A$\frac{4}{9}$
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B$\frac{5}{4}$
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C$\frac{5}{8}$
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D$\frac{5}{9}$
Answer
Correct Answer: $\frac{5}{9}$
Explanation
### Concept & Formula
Total Income consists of basic salary added to the tips received.
$$\text{Total Income} = \text{Salary} + \text{Tips}$$
$$\text{Required Fraction} = \frac{\text{Tips}}{\text{Total Income}}$$
### Step-by-Step Solution
* **Set up relative values:**
Let the basic salary be $S$.
$$\text{Tips} = \frac{5}{4}S$$
* **Calculate the total income:**
$$\text{Total Income} = S + \frac{5}{4}S = \frac{9}{4}S$$
* **Find the proportion originating from tips:**
$$\text{Fraction from Tips} = \frac{\frac{5}{4}S}{\frac{9}{4}S} = \frac{5}{4} \times \frac{4}{9} = \frac{5}{9}$$
### Exam Strategy & Shortcut
Substitute a real value to eliminate variables instantly. Let the salary be ₹ 4 (chosen specifically to clear the denominator of $\frac{5}{4}$).
* Salary = ₹ 4
* Tips = $\frac{5}{4} \times 4 =$ ₹ 5
* Total Income = $4 + 5 =$ ₹ 9
* Fraction from tips = $\frac{5}{9}$
### Common Pitfall
Inverting the ratio values or calculating the fraction relative to basic salary rather than the *total income*, which leads directly to selecting the distractor option $\frac{5}{4}$.
### Final Answer
**Therefore, the correct answer is \frac{5}{9}.**