Question

Madhu and Meena can do a piece of work in $9$ hours. Meena and Mamta can do that it $12$ hours. Madhu and Mamta can do it in $18$ hours.In how many hours will they will finish the work together and separately?

Answer 1

Madhu = A, Meena = B, Mamta = C

From the above conditions

$\frac{1}{A}+\frac{1}{B}=\frac{1}{9}$ ___(1)

$\frac{1}{B}+\frac{1}{C}=\frac{1}{12}$ ___(2)

$\frac{1}{A}+\frac{1}{C}=\frac{1}{18}$ ___(3)

Adding (1),(2) and (3) we get

$\frac{2}{A}+\frac{2}{B}+\frac{2}{C}=\frac{1}{9}+\frac{1}{12}+\frac{1}{18}$

$\Rightarrow 2(\frac{1}{A}+\frac{1}{B}+\frac{1}{C})=\frac{4+3+2}{36}=\frac{9}{36}$

$\Rightarrow \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{1}{8}$

So all together can do it in 8 hrs

$\frac{1}{C}=\frac{1}{8}-\frac{1}{9}=\frac{1}{72}$ So C = 72 hrs

$\frac{1}{B}$ $=\frac{1}{8}-\frac{1}{18}$ $=\frac{18-8}{8\times 18}$ $=\frac{5}{72}$ $\therefore B=\frac{72}{5}=14.4hrs$

$\frac{1}{A}=\frac{1}{8}-\frac{1}{12}=\frac{12-8}{8\times 12}=\frac{4}{8\times 12}=\frac{1}{24}\therefore C=24hrs$