If the income of Ram is 10 % more than that of shyam's income . How much % shyam's income is less than that of Ram's income ?

Answer

To solve the problem step by step, we need to find out how much percentage Shyam's income is less than Ram's income given that Ram's income is 10% more than Shyam's income.

### Step 1: Define the incomes
Let's assume Shyam's income is \( S \).

### Step 2: Calculate Ram's income
Since Ram's income is 10% more than Shyam's income, we can express Ram's income \( R \) as:
\[ R = S + 0.10S = 1.10S \]

### Step 3: Find the difference between Ram's and Shyam's income
The difference between Ram's income and Shyam's income is:
\[ R - S = 1.10S - S = 0.10S \]

### Step 4: Calculate the percentage difference
To find out how much percentage Shyam's income is less than Ram's income, we use the formula:
\[ \text{Percentage difference} = \left( \frac{R - S}{R} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage difference} = \left( \frac{0.10S}{1.10S} \right) \times 100 \]

### Step 5: Simplify the expression
The \( S \) in the numerator and denominator cancels out:
\[ \text{Percentage difference} = \left( \frac{0.10}{1.10} \right) \times 100 \]

### Step 6: Calculate the final value
Now, calculating \( \frac{0.10}{1.10} \):
\[ \frac{0.10}{1.10} = \frac{10}{110} = \frac{1}{11} \]
Thus,
\[ \text{Percentage difference} = \left( \frac{1}{11} \right) \times 100 \approx 9.09\% \]

### Final Answer
Shyam's income is approximately 9.09% less than Ram's income.

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