Let a man do \(\frac{1}{x}\) work per day and

each woman do \(\frac{1}{y}\) work per day

\(\frac{12}{x} + \frac{16}{y} = \frac{1}{5}............\)(1)

\(\frac{13}{x} +\frac{24}{y} = \frac{1}{4}\) ............ (2)

Multiply (1) by 3 & (2) by 2

\(\frac{36}{x} + \frac{48}{y} = \frac{3}{5}\) ....... (3)

\(\frac{26}{x} + \frac{48}{y} = \frac{1}{2}\) ........ (4)

Equation (3) - (4)

\(\frac{10}{x} = \frac{1}{10}\)

x = 100

y = 200

We require to find z; substituting the values

\(\frac{7}{x}+\frac{10}{y}= \frac{1}{z}\)

\(\frac{7}{100}+ \frac{10}{200} = \frac{1}{z}\)

\(\frac{7}{100}+ \frac{5}{100} = \frac{1}{z}\)

\(\frac{12}{100} = \frac{1}{z}\)

\(z = \frac{100}{12} = 8.33 = Answer\)

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