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 X bullocks alone to plough the field?

• A.
  $30$
• B.
  $35$
• C.
  $40$
• D.
  $45$

Answer 1

The correct option is A

$30$
$x\to \text{Bullocks}$
$y\to \text{Tractors}$

$(x+y)8=(\frac{x}{2}+2y)5$

$8x+8y=\frac{5x}{2}+10y$

$\Rightarrow 5.5x=2y\text{or}y=2.75x$

Now, x bullocks are alone working or 'd' days.

$x\times d=(x+y)8$

$x\times d=(x+2.75x)8$

$x\times d=3.75x\times 8$

$d=30$ days