Select the correct answerP can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. Then Q alone can do it in?Options25 days30 days20 days15 days

To solve this problem, we need to understand the concept of work and time, and how they relate to each other in this context.

Step 1: Understand the problem The problem states that P can do a work in the same time in which Q and R together can do it. This means that the work rate of P is equal to the combined work rate of Q and R.

Step 2: Translate the problem into equations We know that work rate is work/time. So, we can write the first condition as: P = Q + R

The problem also states that P and Q together can complete the work in 10 days. This means that the combined work rate of P and Q is 1/10 work/day. We can write this as: P + Q = 1/10

Finally, the problem states that R alone needs 50 days to complete the same work. This means that the work rate of R is 1/50 work/day. We can write this as: R = 1/50

Step 3: Solve the equations We can substitute the value of R from the third equation into the first equation to get: P = Q + 1/50

Then, we can substitute the value of P from this equation into the second equation to get: Q + 1/50 + Q = 1/10 2Q + 1/50 = 1/10 2Q = 1/10 - 1/50 2Q = 4/50 Q = 4/50 / 2 Q = 2/50 Q = 1/25

So, Q alone can do the work in 25 days. Therefore, the correct answer is "25 days".