Math Problem Statement

A can do a piece of work in 20 days and B can do it in 12 days. B worked at it for 9 days. In how many days A alone can finish the remaining work?

Solution

It looks like you've uploaded a math question involving work and time. I'll analyze the questions step by step for clarity.

For Question 9: A can finish the work in 20 days, and B can finish it in 12 days. B worked for 9 days. The question asks how many days A alone will need to finish the remaining work.

We can break it down like this:

  • A's rate of work is 120\frac{1}{20} of the total work per day.
  • B's rate of work is 112\frac{1}{12} of the total work per day.
  • B worked for 9 days, so the work done by B is 9×112=912=349 \times \frac{1}{12} = \frac{9}{12} = \frac{3}{4}.
  • The remaining work is 134=141 - \frac{3}{4} = \frac{1}{4}.

Now, A needs to finish 14\frac{1}{4} of the work. Since A’s rate of work is 120\frac{1}{20}, the time A will take is:

14120=5 days\frac{\frac{1}{4}}{\frac{1}{20}} = 5 \text{ days}

For Question 10: A can do the work in 24 days. If B is 60% more efficient than A, we need to find how many days B would take to do the same work.

B's efficiency is 60% more than A’s, meaning B works 1.6 times faster than A. Therefore, if A takes 24 days, B will take:

241.6=15 days\frac{24}{1.6} = 15 \text{ days}

So, the correct answer to Question 10 is 15 days.

Would you like further explanation on any specific question or concept? Here are some related questions for further practice:

  1. If A completes a task in 15 days and B completes the same task in 25 days, how long would they take together?
  2. If A and B finish a task together in 10 days, and A works alone for 4 days, how many more days does B need to finish the work?
  3. If B is 50% more efficient than A, how much more time does A need to complete the task if they work alone?
  4. A can complete a task in 18 days, and B can complete it in 12 days. If they work together for 6 days, how much work is left?
  5. What is the combined rate of work of two workers, A and B, if A completes the task in 20 days and B completes it in 30 days?

Tip: When solving work problems, always find the individual work rates of the workers involved (work per day) and use them to calculate combined work or remaining work.

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Math Problem Analysis

Mathematical Concepts

Work and Time
Rates of Work
Fractions

Formulas

Work Rate = 1 / Time
Remaining Work = Total Work - Work Done

Theorems

Work done = Rate × Time

Suitable Grade Level

Grades 7-9