Time And Work All Competence Aptitude

Let's first find the rates at which A, B, and C work.

A can complete the job in 15 days, so his rate of work is \( \dfrac{1}{15} \) of the job per day.
B can complete the job in 12 days, so his rate of work is \( \dfrac{1}{12} \) of the job per day.
Together, A, B, and C can complete the job in 5 days, so their combined rate of work is \( \dfrac{1}{5} \) of the job per day.

Let the rate of work of C be \(C\).

Now, since A, B, and C work together, their combined rate of work is the sum of their individual rates of work:

\[ \dfrac{1}{15} + \dfrac{1}{12} + C = \dfrac{1}{5} \]

Now, let's solve for \(C\):

\[ \dfrac{1}{15} + \dfrac{1}{12} + C = \dfrac{1}{5} \]\[ \dfrac{4}{60} + \dfrac{5}{60} + C = \dfrac{12}{60} \]\[ \dfrac{9}{60} + C = \dfrac{12}{60} \]\[ C = \dfrac{12}{60} - \dfrac{9}{60} \]\[ C = \dfrac{3}{60} \]\[ C = \dfrac{1}{20} \]

So, the rate of work of C is \( \dfrac{1}{20} \) of the job per day.

Now, let's find the amount that C earns. Since C works for 5 days, the amount C earns is proportional to the fraction of the work C completes:

\[ \text{Amount earned by C} = \dfrac{\text{Fraction of work completed by C}}{\text{Total fraction of work}} \times \$1200 \]

The fraction of work completed by C in 5 days is \(5 \times \dfrac{1}{20} = \dfrac{1}{4}\). The total fraction of work completed by A, B, and C in 5 days is 1.

So,

\[ \text{Amount earned by C} = \dfrac{\dfrac{1}{4}}{1} \times \$1200 \]\[ \text{Amount earned by C} = \dfrac{1}{4} \times \$1200 \]\[ \text{Amount earned by C} = \$300 \]

Therefore, the share of the amount that C earns is \$300.

First, let's find the work rate of one woman and one man.

Let \( W \) be the work rate of one woman, and \( M \) be the work rate of one man.

Given that 20 women together can complete the work in 16 days, we can find the work rate of one woman:

\[ \text{Work rate of one woman} = \dfrac{1}{20 \times 16} \]

Similarly, given that 16 men together can complete the work in 15 days, we can find the work rate of one man:

\[ \text{Work rate of one man} = \dfrac{1}{16 \times 15} \]

Now, let's calculate these values:

\[ \text{Work rate of one woman} = \dfrac{1}{320} \]\[ \text{Work rate of one man} = \dfrac{1}{240} \]

Now, we can find the ratio of the work rate of a man to that of a woman:

\[ \dfrac{\text{Work rate of one man}}{\text{Work rate of one woman}} = \dfrac{\dfrac{1}{240}}{\dfrac{1}{320}} \]\[ \dfrac{\text{Work rate of one man}}{\text{Work rate of one woman}} = \dfrac{320}{240} \]\[ \dfrac{\text{Work rate of one man}}{\text{Work rate of one woman}} = \dfrac{4}{3} \]

So, the ratio of the working capacity of a man to that of a woman is \(4:3\).

Therefore, the correct answer is \(4:3\).