Question

A is 60% more efficient than



b. in how many days will a and b together complete a piece of work if a alone can complete the work in 15 days

Answer 1

A is 60% more efficient than B.

A can complete the work in 15 days.

In 1 day, A will work = 1/15

let B can finish the work alone in x days

In 1 day, B will work = 1/x

According to the question,

$\frac{ \frac{1}{15} - \frac{1}{x} }{ \frac{1}{x} } \times 100 = 60 \\ \\ \frac{ \frac{1}{15} - \frac{1}{x} }{ \frac{1}{x} } = \frac{6}{10}$

$10 \times (\frac{1}{15} - \frac{1}{x} )=6 \times \frac{1}{x} \\ \\ \frac{10}{15} - \frac{10}{x} = \frac{6}{x}$

$\frac{10}{15} = \frac{10}{x} + \frac{6}{x} = \frac{16}{x} \\ \\ x = 16 \times \frac{15}{10} = 24 \: days$

Thus, B alone can finish in 24 days

in 1 day, he will finish = 1/24

In 1 day, both will finish = 1/15 + 1/24 = 39/360

Number of days needed to finish it together = 360/39 = 120/13 days

They will need 120/13 days to finish it together.