234k views
2 votes
To complete a piece of work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it alone?

a) 18 days
b) 24 days
c) 30 days
d) 36 days

User Dmraptis
by
8.6k points

1 Answer

4 votes

Final answer:

To find how long B will take to work alone, we calculate the work rates of A and B. B's work rate is 1/x and A's is 2/3x. Together, their combined work rate is 1/18, which gives us the equation 5/3x = 1/18. Solving for x gives us 30 days, so B will take 30 days to complete the work alone. Option C is the correct answer.

Step-by-step explanation:

The question requires solving a work rate problem to determine how long it will take for B to complete the work alone. A takes 50% more time than B to complete the same work. To find the time B takes to complete the work alone, we need to understand the concept of work rates and how they combine when two agents are working together.

Let's assume B takes 'x' days to complete the work. This means A takes '1.5x' days (50% more than B). If B does 1 job in 'x' days, B's work rate is 1/x jobs per day. Similarly, A's work rate is 1/1.5x or 2/3x jobs per day.

When A and B work together their work rates add up. So, the combined work rate is 1/x + 2/3x = (3+2)/3x = 5/3x jobs per day. Since together they take 18 days to complete the work, we can equate the combined work rate to 1/18 (because they complete 1 job in 18 days).

Setting up the equation: 5/3x = 1/18. Solving for 'x' we get: x = 5/3 * 18 = 30 days. Therefore, B would take 30 days to complete the work on his own.

The correct answer is Option c) 30 days.

User Robert Ngetich
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories