Total number of mangoes available were consumed by 8 families sharing equal mangoes . Had the mangoes been share by 10 families per familu consumption would have reduced by 8 mangoes . What was the total number of mangoes?

Options

A. data inadequate
B. 320
C. 160
D. 240

Answer

To solve the problem, we will denote the total number of mangoes as \( M \) and the number of mangoes each family receives when shared among 8 families as \( x \).

### Step 1: Set up the equation for 8 families
Since the total number of mangoes \( M \) is shared equally among 8 families, we can express this as:
\[ M = 8x \]

### Step 2: Set up the equation for 10 families
If the same number of mangoes \( M \) is shared among 10 families, then each family would receive \( y \) mangoes. According to the problem, the consumption per family would reduce by 8 mangoes when shared among 10 families:
\[ y = x - 8 \]
Since the total number of mangoes is still \( M \), we can express this as:
\[ M = 10y \]

### Step 3: Substitute \( y \) in the equation
Now we can substitute \( y \) from the previous equation into the equation for \( M \):
\[ M = 10(x - 8) \]

### Step 4: Set the two equations for \( M \) equal to each other
Now we have two expressions for \( M \):
1. \( M = 8x \)
2. \( M = 10(x - 8) \)

Setting them equal gives:
\[ 8x = 10(x - 8) \]

### Step 5: Solve for \( x \)
Expanding the right side:
\[ 8x = 10x - 80 \]
Now, rearranging the equation:
\[ 80 = 10x - 8x \]
\[ 80 = 2x \]
\[ x = 40 \]

### Step 6: Find the total number of mangoes \( M \)
Now that we have \( x \), we can find \( M \):
\[ M = 8x = 8 \times 40 = 320 \]

Thus, the total number of mangoes is \( \boxed{320} \).