Question Details

Two business partners, A and B, share a leased warehouse space. Partner A operates 16 machines for a duration of 6 months. Partner B operates 24 pieces of equipment for 5 months, along with 36 tools for 4 months. Given that the work capacity of 3 machines is equal to that of 6 pieces of equipment, and the capacity of 2 pieces of equipment is equal to that of 3 tools, what fraction of the total warehouse rent should Partner A pay?

Options

$\frac{15}{17}$

$\frac{10}{17}$

$\frac{9}{17}$

$\frac{8}{17}$

Show Answer

Correct Answer :

Option D

$\frac{8}{17}$

Solution :

The correct option is $\frac{8}{17}$ .

To find the fraction of the total warehouse rent that Partner A should pay, we first need to convert the work capacity of all machines, equipment, and tools into a single common unit of work capacity per month.

Let us establish the relationship between the capacities of the different items:

1. The work capacity of 3 machines is equal to that of 6 pieces of equipment:
$3 Machines = 6 Equipment$

Dividing both sides by 3 gives:
$1 Machine = 2 Equipment$

2. The work capacity of 2 pieces of equipment is equal to that of 3 tools:
$2 Equipment = 3 Tools$

Combining these two relationships, we can see that:
$1 Machine = 2 Equipment = 3 Tools$

Let the capacity of 1 tool be equal to 1 unit per month.

From the ratios above:
Capacity of 1 tool = 1 unit/month
Capacity of 1 piece of equipment = $\frac{3}{2}$ units/month = 1.5 units/month
Capacity of 1 machine = 3 units/month

Now, let us calculate the total work units used by each partner (Capacity × Duration):

Partner A's Usage:
Partner A operates 16 machines for 6 months.
Total units for A = $16 \times 3 \times 6 = 288 units$

Partner B's Usage:
Partner B operates 24 pieces of equipment for 5 months, along with 36 tools for 4 months.
Equipment units for B = $24 \times 1.5 \times 5 = 180 units$
Tool units for B = $36 \times 1 \times 4 = 144 units$
Total units for B = $180 + 144 = 324 units$