Question

a+b b+c c+a can complete a work in 10 12 and 15 days respectively. how much days the the work to complete alon​

Answer 1

Answer:

Let days in they complete work be x, y and z for

a, b and c respectively

Given

$\frac{1}{x} + \frac{1}{y} = \frac{1}{10} \\ \frac{1}{y} + \frac{1}{z} = \frac{1}{12} \\ \frac{1}{z} + \frac{1}{x} = \frac{1}{15} \\ solve \\ substract \: eq2 \: from \: eq1 \: and \: add \: \: eq3 \\ \frac{2}{x} = \frac{1}{10} - \frac{1}{12} + \frac{1}{15} = \frac{6 - 5 + 4}{60} \\ x = 24 \: days \\ from \: \: eq1 \\ y = \frac{24 \times 10}{24 - 10} \approx17.14 \: \: days \\ from \: \: eq3 \\ z = \frac{15 \times 24}{24 - 15} = 40 \: \: days$