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A can do a piece of work in 25 days , which B alone can do in 20 days. A staried the work and was joined by B after 10 days. The work lasted for

A. 12 1/2 days
B. 15 days
C. 16 2/3 days
D. 14 days

User Daemone
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1 Answer

4 votes

Final answer:

The work lasted for approximately 13 3/4 days, which is closest to option D - 14 days.

Step-by-step explanation:

To solve this problem, we need to find the individual rates of work for A and B. Let's assume that the total work is represented by the variable W.

We know that A can complete the work in 25 days, so his rate of work is 1/25 of the total work per day. Similarly, B can complete the work in 20 days, so his rate of work is 1/20 of the total work per day.

A started the work and was joined by B after 10 days. So, A worked alone for 10 days and B worked for the remaining days until the work was completed.

Let's calculate the work done by A alone and B alone:

A's work = (A's rate of work) * (number of days A worked) = (1/25) * 10 = 10/25 = 2/5

B's work = (B's rate of work) * (number of days B worked) = (1/20) * (total days - 10) = (1/20) * (25 - 10) = (1/20) * 15 = 3/20

The total work done is the sum of A's work and B's work:

Total work = A's work + B's work = 2/5 + 3/20 = 8/20 + 3/20 = 11/20

The work lasted for 11/20 of the total number of days:

Total number of days = 25

Number of days the work lasted = (11/20) * 25 = 275/20 = 13 3/4 days

So, the work lasted for approximately 13 3/4 days which is closest to option D - 14 days.

User Datum Geek
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