A man saves the same amount each year and now he has Rs. 1200 saved. In four years' time he will have three times as much saved as he had four years ago. How much does he same each year ?

Options

A. Rs. 120
B. Rs.100
C. Rs. 150
D. Rs. 200

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Define the variables
Let the amount the man saves each year be \( x \).

### Step 2: Current savings
According to the problem, the man currently has Rs. 1200 saved.

### Step 3: Calculate future savings
In four years, the total amount he will have saved can be calculated as:
\[ \text{Total savings after 4 years} = \text{Current savings} + \text{Savings in 4 years} \]
This can be expressed as:
\[ 1200 + 4x \]

### Step 4: Calculate past savings
To find out how much he had saved four years ago, we need to subtract the total savings he would have made in those four years from his current savings:
\[ \text{Savings 4 years ago} = \text{Current savings} - \text{Savings in 4 years} = 1200 - 4x \]

### Step 5: Set up the equation
According to the problem, the amount he will have after 4 years will be three times what he had four years ago:
\[ 1200 + 4x = 3 \times (1200 - 4x) \]

### Step 6: Expand and simplify the equation
Expanding the right side of the equation gives:
\[ 1200 + 4x = 3600 - 12x \]

### Step 7: Rearranging the equation
Now, we will bring all terms involving \( x \) to one side and constant terms to the other side:
\[ 4x + 12x = 3600 - 1200 \]
This simplifies to:
\[ 16x = 2400 \]

### Step 8: Solve for \( x \)
Now, divide both sides by 16 to find \( x \):
\[ x = \frac{2400}{16} = 150 \]

### Conclusion
The man saves Rs. 150 each year.

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