`2/5` of a number exceeds `2/7` of the number by 40. Find the number.

Options

A. 250
B. 280
C. 320
D. 350

Answer

To solve the problem step by step, let's denote the unknown number as \( a \).

### Step 1: Set up the equation
According to the problem, \( \frac{2}{5} \) of the number exceeds \( \frac{2}{7} \) of the number by 40. We can express this relationship as:
\[ \frac{2}{5}a = \frac{2}{7}a + 40 \]

### Step 2: Rearranging the equation
To solve for \( a \), we need to isolate \( a \) on one side of the equation. We can do this by subtracting \( \frac{2}{7}a \) from both sides:
\[ \frac{2}{5}a - \frac{2}{7}a = 40 \]

### Step 3: Finding a common denominator
To combine the fractions on the left side, we need a common denominator. The least common multiple (LCM) of 5 and 7 is 35. We can rewrite the fractions:
\[ \frac{2}{5}a = \frac{2 \times 7}{5 \times 7}a = \frac{14}{35}a \]
\[ \frac{2}{7}a = \frac{2 \times 5}{7 \times 5}a = \frac{10}{35}a \]
Now, substituting these back into the equation gives:
\[ \frac{14}{35}a - \frac{10}{35}a = 40 \]

### Step 4: Simplifying the equation
Now we can combine the fractions:
\[ \frac{14 - 10}{35}a = 40 \]
\[ \frac{4}{35}a = 40 \]

### Step 5: Solving for \( a \)
To isolate \( a \), multiply both sides by \( \frac{35}{4} \):
\[ a = 40 \times \frac{35}{4} \]
Calculating this gives:
\[ a = 40 \times 8.75 = 350 \]

### Final Answer
Thus, the number is:
\[ \boxed{350} \]