A and B borrowed a tractor for 23 days. A ploughed 12 acres per day for a certain number of days and then Bused it to plough 15 acres per day for the remaining days, If they paid Rs 3, and Rs 2,0 respectively, for how many days did A use the tractor?

Options

A. 12
B. 15
C. 16
D. 18

Answer

To solve the problem, we need to find out how many days A used the tractor. Let's break down the solution step by step.

### Step 1: Define Variables
Let \( X \) be the number of days A used the tractor.

### Step 2: Determine B's Usage
Since A used the tractor for \( X \) days, B used it for the remaining days. The total duration is 23 days, so:
\[ \text{Days B used} = 23 - X \]

### Step 3: Calculate Total Acres Ploughed
A ploughed 12 acres per day for \( X \) days, so the total acres ploughed by A is:
\[ \text{Acres by A} = 12X \]
B ploughed 15 acres per day for \( 23 - X \) days, so the total acres ploughed by B is:
\[ \text{Acres by B} = 15(23 - X) \]

### Step 4: Set Up the Payment Equation
According to the problem, A paid Rs 3 for each acre he ploughed, and B paid Rs 2 for each acre he ploughed. Therefore, we can set up the equation based on the payments:
\[ 3(12X) = 2(15(23 - X)) \]

### Step 5: Simplify the Equation
Expanding both sides gives:
\[ 36X = 30(23 - X) \]
\[ 36X = 690 - 30X \]

### Step 6: Combine Like Terms
Adding \( 30X \) to both sides:
\[ 36X + 30X = 690 \]
\[ 66X = 690 \]

### Step 7: Solve for X
Now, divide both sides by 66:
\[ X = \frac{690}{66} = 10.45 \]
Since \( X \) must be a whole number, we round down to 10 (assuming A used the tractor for full days).

### Step 8: Conclusion
A used the tractor for approximately 10 days.