After an increment of `16 (2)/( 3) %` the cost of a machine, it becomes Rs. 4900. Find the initial cost of machine.

Answer

To find the initial cost of the machine after a percentage increase, we can follow these steps:

### Step 1: Convert the percentage to a fraction
The percentage increase given is \( 16 \frac{2}{3} \% \). We can convert this mixed number into an improper fraction:
\[ 16 \frac{2}{3} = \frac{50}{3} \% \]
This means the increase is \( \frac{50}{3} \) percent.

### Step 2: Convert the percentage to a decimal
To use this percentage in calculations, we convert it to a decimal by dividing by 100:
\[ \frac{50}{3} \div 100 = \frac{50}{300} = \frac{1}{6} \]
This indicates that the cost of the machine has increased by \( \frac{1}{6} \) of its original price.

### Step 3: Determine the relationship between the original and final cost
Let the original cost of the machine be \( x \). After the increase, the new cost becomes:
\[ x + \frac{1}{6}x = \frac{7}{6}x \]
We know that this new cost is equal to Rs. 4900:
\[ \frac{7}{6}x = 4900 \]

### Step 4: Solve for the original cost \( x \)
To find \( x \), we can multiply both sides of the equation by \( \frac{6}{7} \):
\[ x = 4900 \times \frac{6}{7} \]
Calculating this gives:
\[ x = 4900 \times \frac{6}{7} = 4900 \times 0.857142857 \approx 4200 \]

### Step 5: Conclusion
The initial cost of the machine is Rs. 4200.

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