A is Twice as Good a Workman as B and Together They Finish a Piece GMAT Problem Solving

Question: A is twice as good a workman as B and together they finish a piece of work in 16 days. In how many days will A alone finish the work?

(A) 20 days
(B) 23 days
(C) 24 days
(D) 25 days
(E) 27 days

Correct Answer: C

Solution and Explanation:
Approach Solution 1:
The problem statement states that:
Given:

• A is twice as good a workman as B and together they finish a piece of work in 16 days.

Find out:

• The number of days A alone will finish the work.

The given sum can be solved by using the mathematical equation of work, time and efficiency. The problem given illustrates that the Efficiency of A equals that of 2 times of Efficiency of B. They together can complete the whole work in 18 days.

Hence using the formula: Work = Efficiency × Time.
The calculation goes like this:
Efficiency of A: Efficiency of B = 2: 1
Efficiency of (A + B) = 3
Total Work = 3 x 16 = 48 units
A alone can do this work in 48/2 days [Total work/efficiency of A]= 24 days.
Therefore, the time taken by A to complete the work is 24 days.

Approach Solution 2:
The problem statement implies that:
Given:

• A is twice as good a workman as B and together they finish a piece of work in 16 days.

Find out:

• The number of days A alone will finish the work.

Let’s consider that B does x [p.o.w/day] and A does 2x [p.o.w/day].
Here. where p.o.w stands for pieces of work.

Now, we know that together they finish 1 p.o.w in 16 days.
Putting the information in an equation, we have

(x+2x) \(\frac {p.o.w}{day}*16days=1p.o.w\)

\(x=\frac{1}{48}\frac{p.o.w}{day}\)

Now, we know that B does 1/48 [p.o.w/day]and A does 2/48 [p.o.w/day].
Finally, to find in how many days A alone will finish 1p.o.w we can use

\(\frac{2}{48}\frac{p.o.w}{day}*y days= 1 p.o.w\)

y = 24 days
Hence, A will finish in 24 days one piece of work.

Approach Solution 3:
The problem statement suggests that:
Given:

• A is twice as good a workman as B and together they finish a piece of work in 16 days.

Find out:

• The number of days A alone will finish the work.

As per the condition of the question, A : B = 2 : 1
=> A = 2/3

A and B together finish a piece of work in 16 days.
Therefore, work done by A+B= 1/16.

Therefore, work done by A alone = 2/3 * 1/16 = 2/48 = 1/24

 Hence, the number of days A alone will finish the work = 24 days.

“A is twice as good a workman as B and together they finish a piece”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. To solve the GMAT Problem Solving questions, the candidates must have a basic knowledge of arithmetic, geometry and algebra. The candidates can follow the GMAT Quant practice papers to practise varieties of questions that will help them to improve their mathematical skills.

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