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?
 ${\text{A}}{\text{. }}\dfrac{{20}}{9}$ days
${\text{B}}{\text{. }}\dfrac{{11}}{9}$ days
${\text{C}}{\text{. }}3$ days
${\text{D}}{\text{. }}$None of these

Answer 1

Hint: Here, we will proceed by finding out the number of days taken by A, B and C separately to complete the work or job and then we will use the unitary method to find out the amount of the work done by A, B and C separately in 1 day.

Complete step-by-step answer:

Given, B finishes the total work in 10 days.
i.e., Number of days taken by B to finish the work = 10 days
Given that A is thrice as efficient as B.

So, Number of days taken by A to finish the work = $\dfrac{{{\text{Number of days taken by B to finish the work}}}}{3} = \dfrac{{10}}{3}$ days

Amount of the work done by B in 1 day = $\dfrac{1}{{10}}$

Amount of the work done by A in 1 day = $\dfrac{1}{{\left( {\dfrac{{10}}{3}} \right)}} = \dfrac{3}{{10}}$

Also, given that B is twice efficient as C.

So, Number of days taken by B to finish the work = $\dfrac{{{\text{Number of days taken by C to finish the work}}}}{2}$
$ \Rightarrow $Number of days taken by C to finish the work = 2(Number of days taken by B to finish the work)
$ \Rightarrow $Number of days taken by C to finish the work = 2(10) = 20 days

Amount of the work done by C in 1 day = $\dfrac{1}{{20}}$

As we know that,
Amount of work done in 1 day when A, B and C work together = (Amount of the work done by A in 1 day) + (Amount of the work done by B in 1 day) + (Amount of the work done by C in 1 day)
$ \Rightarrow $Amount of work done in 1 day when A, B and C work together $ = \dfrac{3}{{10}} + \dfrac{1}{{10}} + \dfrac{1}{{20}} = \dfrac{{\left( {3 \times 2} \right) + \left( {1 \times 2} \right) + 1}}{{20}} = \dfrac{{6 + 2 + 1}}{{20}} = \dfrac{9}{{20}}$

Number of days taken to finish the work when A, B and C work together = $\dfrac{1}{{\dfrac{9}{{20}}}} = \dfrac{{20}}{9}$ days

Hence, option A is correct.

Note: In this particular problem, A is thrice as efficient as B means that the number of days taken by B is three times the number of days taken by A to finish the work. Here, we have used a unitary method in order to convert the number of days taken into the piece of work or the amount of work done in 1 day.