Question

Let s, m and f denote the respective time taken by son, mother and father to complete the work
If $\frac{1}{s}+\frac{1}{m}=\frac{1}{24},\frac{1}{s}+\frac{1}{f}=\frac{1}{18}and\frac{1}{m}+\frac{1}{f}=\frac{1}{36}$
then find $\frac{1}{s}+\frac{1}{m}+\frac{1}{f}and\frac{1}{s},\frac{1}{m},\frac{1}{f}$ respectively

• A. $\frac{1}{16},\frac{1}{144},\frac{5}{144},\frac{3}{144}$
• B. $\frac{1}{16},\frac{5}{144},\frac{1}{144},\frac{3}{144}$
• C. $\frac{1}{16},\frac{3}{144},\frac{1}{144},\frac{5}{144}$
• D. None of these

Answer 1

The correct option is B $\frac{1}{16},\frac{5}{144},\frac{1}{144},\frac{3}{144}$

As given
$\frac{1}{s}+\frac{1}{m}=\frac{1}{24}$,----eq1
$\frac{1}{s}+\frac{1}{f}=\frac{1}{18}$ -------eq2
$\frac{1}{m}+\frac{1}{f}=\frac{1}{36}$ ----------eq3
By adding all the 3 equation we get,
$\frac{2}{s}+\frac{2}{m}+\frac{2}{f}=\frac{1}{24}+\frac{1}{18}+\frac{1}{36}$
$\frac{2}{s}+\frac{2}{m}+\frac{2}{f}=\frac{3+4+2}{72}$
$\frac{1}{s}+\frac{1}{m}+\frac{1}{f}=\frac{9}{144}$
$\frac{1}{s}+\frac{1}{m}+\frac{1}{f}=\frac{1}{16}$-- eq 4
by subtracting eq1 from eq4 we get $\frac{1}{f}$
$\frac{1}{s}+\frac{1}{m}+\frac{1}{f}-\frac{1}{s}-\frac{1}{m}=\frac{1}{16}-\frac{1}{24}$
$\frac{1}{f}=\frac{1}{48}=\frac{3}{144}$
by subtracting eq2 from eq4 we get $\frac{1}{m}$
$\frac{1}{s}+\frac{1}{m}+\frac{1}{f}-\frac{1}{s}-\frac{1}{f}=\frac{1}{16}-\frac{1}{18}$
$\frac{1}{m}=\frac{1}{144}$
by subtracting eq3 from eq4 we get $\frac{1}{s}$
$\frac{1}{s}+\frac{1}{m}+\frac{1}{f}-\frac{1}{m}-\frac{1}{f}=\frac{1}{16}-\frac{1}{36}$
$\frac{1}{s}=\frac{5}{144}$
Answer (B) $\frac{1}{16},\frac{5}{144},\frac{1}{144},\frac{3}{144}$