A village lost `12%` of the goats in flood and `5%` of remaining died from diseases. If the no. left is now `8360`. What was the original no. before the flood ?

Options

A. `12,000`
B. `10,000`
C. `11,000`
D. `14,000`

Answer

To find the original number of goats before the flood, we can follow these steps:

### Step 1: Define the original number of goats
Let the original number of goats before the flood be \( x \).

### Step 2: Calculate the number of goats after the flood
The village lost 12% of the goats in the flood. Therefore, the percentage of goats that remained after the flood is:
\[ 100\% - 12\% = 88\% \]
So, the number of goats remaining after the flood is:
\[ \text{Remaining goats} = x \times \frac{88}{100} = 0.88x \]

### Step 3: Calculate the number of goats after disease
Out of the remaining goats, 5% died from diseases. Thus, the percentage of goats that survived after the disease is:
\[ 100\% - 5\% = 95\% \]
So, the number of goats left after the disease is:
\[ \text{Goats left after disease} = 0.88x \times \frac{95}{100} = 0.88x \times 0.95 = 0.836x \]

### Step 4: Set up the equation
According to the problem, the number of goats left after the flood and disease is 8,360. Therefore, we can set up the equation:
\[ 0.836x = 8360 \]

### Step 5: Solve for \( x \)
To find \( x \), we divide both sides of the equation by 0.836:
\[ x = \frac{8360}{0.836} \]
Calculating this gives:
\[ x = 10000 \]

### Conclusion
The original number of goats before the flood was \( 10,000 \).

---