Mr AM, the magnanimous cashier at XYZ Ltd., while distributing salary, adds whatever money is needed to make the sum a multiple of 50. He adds '10 and ' 40 to A's and B's salary respectively and then he realises that the salaries of A, B and C are now in the ratio 4 : 5 : 7 The salary of C could be

Options

A. A)`'2300`
B. B)`'2150`
C. C)`'1800`
D. D)`'2100`

Answer

To solve the problem, we need to determine the salary of C based on the information provided about the salaries of A, B, and C after Mr. AM adjusts them to be multiples of 50.

### Step-by-Step Solution:

1. **Understanding the Adjustments**:
- Let A's original salary be \( a \).
- Mr. AM adds 10 to A's salary, making it \( a + 10 \).
- Let B's original salary be \( b \).
- Mr. AM adds 40 to B's salary, making it \( b + 40 \).
- Let C's original salary be \( c \) (no adjustment is made).

2. **Setting Up the Ratio**:
- After the adjustments, the salaries of A, B, and C are in the ratio 4:5:7.
- This can be expressed as:
\[ a + 10 : b + 40 : c = 4 : 5 : 7 \]

3. **Expressing Salaries in Terms of a Common Variable**:
- Let the common multiple be \( k \). Thus, we can write:
\[ a + 10 = 4k \]
\[ b + 40 = 5k \]
\[ c = 7k \]

4. **Expressing A's and B's Salaries**:
- From the equations above, we can express A's and B's original salaries:
\[ a = 4k - 10 \]
\[ b = 5k - 40 \]

5. **Finding the Values of k**:
- Since A's and B's salaries must also be multiples of 50 after the adjustments, we need to ensure that \( a + 10 \) and \( b + 40 \) are multiples of 50.
- Therefore:
\[ 4k \equiv 0 \, (\text{mod } 50) \]
\[ 5k \equiv 0 \, (\text{mod } 50) \]

6. **Finding Possible Values for k**:
- The least common multiple of 4 and 5 is 20, so \( k \) must be a multiple of 10 to satisfy both conditions.
- Let’s check the multiples of 10: \( k = 10, 20, 30, \ldots \)

7. **Calculating C's Salary**:
- Now, we substitute \( k \) back into the equation for C's salary:
\[ c = 7k \]
- Possible values for C's salary based on \( k \):
- If \( k = 10 \), \( c = 70 \)
- If \( k = 20 \), \( c = 140 \)
- If \( k = 30 \), \( c = 210 \)
- If \( k = 40 \), \( c = 280 \)
- If \( k = 50 \), \( c = 350 \)
- If \( k = 60 \), \( c = 420 \)
- If \( k = 70 \), \( c = 490 \)
- If \( k = 80 \), \( c = 560 \)
- If \( k = 90 \), \( c = 630 \)
- If \( k = 100 \), \( c = 700 \)
- If \( k = 110 \), \( c = 770 \)
- If \( k = 120 \), \( c = 840 \)
- If \( k = 130 \), \( c = 910 \)
- If \( k = 140 \), \( c = 980 \)
- If \( k = 150 \), \( c = 1050 \)
- If \( k = 160 \), \( c = 1120 \)
- If \( k = 170 \), \( c = 1190 \)
- If \( k = 180 \), \( c = 1260 \)
- If \( k = 190 \), \( c = 1330 \)
- If \( k = 200 \), \( c = 1400 \)
- If \( k = 210 \), \( c = 1470 \)
- If \( k = 220 \), \( c = 1540 \)
- If \( k = 230 \), \( c = 1610 \)
- If \( k = 240 \), \( c = 1680 \)
- If \( k = 250 \), \( c = 1750 \)
- If \( k = 260 \), \( c = 1820 \)
- If \( k = 270 \), \( c = 1890 \)
- If \( k = 280 \), \( c = 1960 \)
- If \( k = 290 \), \( c = 2030 \)
- If \( k = 300 \), \( c = 2100 \)

8. **Checking the Options**:
- The options given are:
- Option A: 2300
- Option B: 2150
- Option C: 1800
- Option D: 2100
- Among these, only 2100 is a multiple of 300 (which is \( 7 \times 300 \)), thus it is a valid salary for C.

### Conclusion:
The salary of C could be **2100**.