Question

X bullocks and Y tractors take 8 days to plough a field. If we halve the number of bullocks and double the number of tractors, it takes 5 days to plough the same field. How many days will it take for X bullocks alone to plough the field ?

• A. 30
• B. 35
• C. 40
• D. 45

Answer 1

The Correct Option is A

Let's start by defining the productivity of bullocks and tractors. Let the productivity of 1 bullock be \( B \) and 1 tractor be \( T \). Since \( X \) bullocks and \( Y \) tractors together can plough the field in 8 days, their collective productivity is \( \frac{1}{8} \) of the work (the whole field) per day. Therefore, we write: 

\( X \cdot B + Y \cdot T = \frac{1}{8} \)

 

When we halve the number of bullocks (i.e., \( \frac{X}{2} \)) and double the number of tractors (i.e., \( 2Y \)), the new scenario takes 5 days, giving us:

\( \frac{X}{2} \cdot B + 2Y \cdot T = \frac{1}{5} \)

 

We now have two equations to solve for \( B \) and \( T \):

1) \( X \cdot B + Y \cdot T = \frac{1}{8} \)

 

2) \( \frac{X}{2} \cdot B + 2Y \cdot T = \frac{1}{5} \)

 

Multiply equation (1) by 2:

\( 2X \cdot B + 2Y \cdot T = \frac{1}{4} \)

 

Substitute this into equation (2):

\( \frac{X}{2} \cdot B + 2Y \cdot T = \frac{1}{5} \)

 

Subtract the second equation from the scaled equation (1):

\( (2X \cdot B + 2Y \cdot T) - (\frac{X}{2} \cdot B + 2Y \cdot T) = \frac{1}{4} - \frac{1}{5} \)

 

Simplify the left-hand side:

\( \frac{3X}{2} \cdot B = \frac{1}{20} \)

 

Solving for \( B \):

\( B = \frac{1}{30X} \)

 

To find how many days \( X \) bullocks will take to plough the field alone, we use:

\( X \cdot B = \frac{1}{D} \)

 

Substitute \( B \) from above:

\( X \cdot \frac{1}{30X} = \frac{1}{D} \)

 

Simplifying gives:

\( \frac{1}{30} = \frac{1}{D} \)

 

Therefore, \( D = 30 \).

The number of days it will take for \( X \) bullocks alone to plough the field is 30.