`(1)/(5)` of a number exceeds `(1)/(7)` of the same number by 10.The number is :

Options

A. 125
B. 150
C. 175
D. 200

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Define the variable
Let the number be \( x \).

### Step 2: Set up the equation
According to the problem, \( \frac{1}{5} \) of the number exceeds \( \frac{1}{7} \) of the same number by 10. This can be expressed mathematically as:
\[ \frac{1}{5}x - \frac{1}{7}x = 10 \]

### Step 3: Find a common denominator
To solve the equation, we need to find a common denominator for the fractions. The least common multiple (LCM) of 5 and 7 is 35. We will rewrite the fractions with this common denominator:
\[ \frac{7}{35}x - \frac{5}{35}x = 10 \]

### Step 4: Combine the fractions
Now, we can combine the fractions on the left side:
\[ \frac{7x - 5x}{35} = 10 \]
This simplifies to:
\[ \frac{2x}{35} = 10 \]

### Step 5: Cross-multiply to eliminate the fraction
To eliminate the fraction, we can cross-multiply:
\[ 2x = 10 \times 35 \]

### Step 6: Calculate the right side
Now, calculate \( 10 \times 35 \):
\[ 10 \times 35 = 350 \]
So, we have:
\[ 2x = 350 \]

### Step 7: Solve for \( x \)
Now, divide both sides by 2 to find \( x \):
\[ x = \frac{350}{2} = 175 \]

### Final Answer
The number is \( 175 \).