What is the monthly income of Mr.X?
I. Mr.X spends `85%` of his income on various items and remaining amount is saved.
II. Monthly saving of Mr. X is Rs 4,500/.
III. Out of the total money spent by Mr. X in a month, one fifth is spent on food and remaining amount of Rs.20, 400 on other items. (a) Only ll (b) Only lll (c) only either l or ll (d) None of these

Options

A. Only II
B. Only III
C. Onlt either II or III
D. None of these

Explanation

To determine Mr. X's monthly income, we need to analyze the statements provided:

### Step-by-Step Solution:

1. **Understanding Statement I**:
- Mr. X spends 85% of his income on various items, and the remaining amount is saved.
- Let's denote Mr. X's monthly income as \( I \).
- According to this statement, the amount saved is \( 15\% \) of \( I \) (since \( 100\% - 85\% = 15\% \)).
- Therefore, the saving can be expressed as:
\[ \text{Savings} = 0.15I \]

2. **Understanding Statement II**:
- The monthly saving of Mr. X is Rs 4,500.
- From Statement I, we have:
\[ 0.15I = 4500 \]
- To find \( I \), we can rearrange the equation:
\[ I = \frac{4500}{0.15} = 30,000 \]
- Thus, from Statement II alone, we can determine Mr. X's monthly income.

3. **Understanding Statement III**:
- Out of the total money spent by Mr. X in a month, one-fifth is spent on food, and the remaining amount of Rs 20,400 is spent on other items.
- Let’s denote the total expenditure as \( E \).
- According to this statement:
\[ \frac{1}{5}E + 20,400 = E \]
- Rearranging gives:
\[ 20,400 = E - \frac{1}{5}E = \frac{4}{5}E \]
- Therefore, we can find \( E \):
\[ E = \frac{20,400 \times 5}{4} = 25,500 \]
- Now, since Mr. X spends 85% of his income on various items, we can set up the equation:
\[ 0.85I = 25,500 \]
- Rearranging gives:
\[ I = \frac{25,500}{0.85} = 30,000 \]
- Thus, from Statement III alone, we can also determine Mr. X's monthly income.

### Conclusion:
- Both Statement II and Statement III provide sufficient information to determine Mr. X's monthly income, which is Rs 30,000.
- Therefore, the correct answer is **(c) only either I or II**.