Maitreyee was given some money to take care of her travel during a 10-day sales drive she had to undertake. However, she had to increase her stay by another 6 days, and as a result, her average daily travel allowance went down by Rs.45. What was the amount that was sanctioned to her in the beginning?

Options

A. Rs.1,120
B. Rs.1,200
C. Rs.960
D. Rs.1,040

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Define the variables
Let the total amount of money sanctioned to Maitreyee be \( X \).

### Step 2: Calculate the average daily allowance for the initial 10 days
The average daily travel allowance for the initial 10 days is given by:
\[ \text{Average for 10 days} = \frac{X}{10} \]

### Step 3: Calculate the average daily allowance for the extended 16 days
If Maitreyee extends her stay to 16 days, her average daily travel allowance becomes:
\[ \text{Average for 16 days} = \frac{X}{16} \]

### Step 4: Set up the equation based on the decrease in average allowance
According to the problem, the average daily allowance decreases by Rs. 45 when she stays for 16 days. Therefore, we can set up the equation:
\[ \frac{X}{10} - \frac{X}{16} = 45 \]

### Step 5: Solve the equation
To solve this equation, we first find a common denominator for the fractions. The least common multiple of 10 and 16 is 80. Thus, we rewrite the equation:
\[ \frac{8X}{80} - \frac{5X}{80} = 45 \]
This simplifies to:
\[ \frac{3X}{80} = 45 \]

### Step 6: Isolate \( X \)
To isolate \( X \), multiply both sides by 80:
\[ 3X = 45 \times 80 \]
Calculating the right side:
\[ 3X = 3600 \]
Now, divide by 3:
\[ X = \frac{3600}{3} = 1200 \]

### Conclusion
The amount that was sanctioned to Maitreyee in the beginning is **Rs. 1200**.

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