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P can do a piece of work in x days and Q can do the same work 3x days. To finish the work together they take 12 days. What is the value of x?

Question

P can do a piece of work in x days and Q can do the same work 3x days. To finish the work together they take 12 days. What is the value of x?

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Solution

Let's solve this step by step:

Step 1: Understand the problem P can do a piece of work in x days and Q can do the same work in 3x days. Together they take 12 days to finish the work. We need to find the value of x.

Step 2: Set up the equations We know that work done is inversely proportional to the time taken. So, the work done by P in one day is 1/x and the work done by Q in one day is 1/(3x).

When they work together, they can finish the work in 12 days. So, the combined work done by P and Q in one day is 1/12.

Step 3: Write the equation So, we can write the equation as: 1/x + 1/(3x) = 1/12

Step 4: Solve the equation To solve for x, we first get rid of the fractions by multiplying the entire equation by 12x, which gives: 12 + 4 = x

Step 5: Solve for x So, x = 16 days.

This problem has been solved

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