Select the correct answerWorking together, Asha and Sudha can complete an assigned task in 20 days. However, if Asha worked alone and completed half the work and then Sudha takes over the task and completes the second half of the task, the task will be completed in 45 days. How long will Asha take to complete the task if she worked alone? Assume that Sudha is more efficient than Asha.Options25 days60 days65 days30 days
Question
Select the correct answerWorking together, Asha and Sudha can complete an assigned task in 20 days. However, if Asha worked alone and completed half the work and then Sudha takes over the task and completes the second half of the task, the task will be completed in 45 days. How long will Asha take to complete the task if she worked alone? Assume that Sudha is more efficient than Asha.Options25 days60 days65 days30 days
Solution
This problem can be solved using the concept of work and efficiency in time and work problems.
Step 1: Let's denote the time taken by Asha to complete the task alone as 'A' and the time taken by Sudha to complete the task alone as 'S'.
Step 2: We know that Asha and Sudha together can complete the task in 20 days. So, their combined rate of work is 1/20 of the task per day.
Step 3: We also know that if Asha completes half the task and then Sudha completes the other half, it takes 45 days. This means that Asha takes 45 days to complete half the task, so she would take 90 days to complete the whole task alone. So, A = 90.
Step 4: Since Asha and Sudha together can complete 1/20 of the task per day, and we know Asha's rate of work is 1/90 of the task per day, we can find Sudha's rate of work by subtracting Asha's rate from their combined rate. So, Sudha's rate of work is 1/20 - 1/90 = 1/30 of the task per day.
Step 5: This means that Sudha would take 30 days to complete the task alone. But we are asked to find how long Asha would take, and we found earlier that A = 90.
So, Asha would take 90 days to complete the task alone. However, this option is not given in the question. There might be a mistake in the question or the options provided.
Similar Questions
A can do work in 20 days. Then, he is assisted by B to complete the remaining work in 12 days. In how much time can B alone do the work?
When they work alone, B needs 60% more time to finish a piece of work than A does. Both of them finish the work in the following manner: B works alone till one-fourth of the work is done, then A and B work together for 12 days, and finally, A works alone to complete the remaining 10% of the work. In how many days can A alone finish the entire work?
Select the correct answerA, B and C can do a piece of work in 30 days, 45 days and 90 days, respectively. A starts the work and he is assisted by B and C together on every third day. In how many days will the work be completed?Options24233022
A can do a piece of work in 80 days. He works on it for 10 days and then B alone finishes the remaining work in 42 days. In how much time will A and B working together, finish the work?A 40 days B 30 days C 60 days D 50 days
A and B together can complete a piece of work in 35 days, while A alone can complete it in 60 days. So, B alone can complete the work in how many days?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.