Question

A is thrice as efficient as B and B is twice as efficient as C. If A, B and C work together, how long will they take to complete a job which B completes in $10$ days?

• A. $\frac{20}{9}$ days
• B. $\frac{11}{9}$ days
• C. $3$ days
• D. None of these

Answer 1

The correct option is A $\frac{20}{9}$ days

Let the time taken by A = $x$ days

$\therefore$ work done by A in $1$ day = $\frac{1}{x}$

A is thrice as efficient as B.

$\Rightarrow$ time taken by B $=3\times$ time taken by A = $3x$ days

$\Rightarrow$ work done by B in $1$ day = $\frac{1}{3x}$

B is twice as efficient as C.

$\Rightarrow$ work done by C in $1$ day = $\frac{1}{6x}$

$\Rightarrow$ time taken by C $=2\times$ time taken by B $=2\times 3x=6x$ days

According to the question-

B completes the job in 10 days

$3x=10$

$\Rightarrow x=\frac{10}{3}$

Work done of 1 day if A, B and C work together-

$\frac{1}{x}+\frac{1}{3x}+\frac{1}{6x}=\frac{3}{10}+\frac{3}{30}+\frac{3}{60}=\frac{18+6+3}{60}=\frac{27}{60}=\frac{9}{20}$

Hence, time taken to complete the job if A, B and C work together $=\frac{20}{9}$ days