Amal completes 75% of the work in 45 days and Pavithra completes the ...
Amal alone complete whole work = 4/3 * 45 = 60 days
PAvithra alone complete work = 120 days
A + B together complete the work in 15 days is = 15/60 + 15/120
= 45/120 = ⅜
Remaining work = 1 – 3/8 = ⅝
Sheela + Divya together can complete 5/8 of the work in 45 days
Sheela + Divya together can complete whole work in 8/5 * 45 = 72 days
Divya alone complete 50% of the work in 72 days
Divya alone complete whole work = 100/50 * 72 = 144 days
Sheela alone complete = 1/72 – 1/144 = 1/144
Amal completes 75% of the work in 45 days and Pavithra completes the ...
To solve this problem, let's break it down into steps:
Step 1: Find the individual work rates of Amal and Pavithra
- We are given that Amal completes 75% of the work in 45 days. This means that in 45 days, Amal completes 3/4 of the work.
- Let's assume the total work is represented by 1 unit. So, Amal completes 3/4 of the work in 45 days, which means he completes 3/4 * 1 = 3/4 of the work in 45 days.
- Therefore, the work completed by Amal in 1 day is 3/4 * 1/45 = 1/60 units.
- Similarly, we are given that Pavithra completes the work in 120 days. So, Pavithra's work rate is 1/120 units per day.
Step 2: Find the work done by Amal and Pavithra together in 15 days
- Since Amal's work rate is 1/60 units per day and Pavithra's work rate is 1/120 units per day, their combined work rate is 1/60 + 1/120 = 1/40 units per day.
- In 15 days, their combined work is 15 * 1/40 = 3/8 units.
Step 3: Find the work done by Sheela and Divya in 45 days
- After Amal and Pavithra left, the remaining work is completed by Sheela and Divya in 45 days. Let's assume their combined work rate is x units per day.
- In 45 days, their combined work is 45 * x = 5/8 units.
Step 4: Find Divya's work rate
- We are given that Divya alone completes 50% of the work in 72 days. This means that Divya completes 1/2 of the work in 72 days.
- Divya's work rate is 1/2 * 1/72 = 1/144 units per day.
Step 5: Find Sheela's work rate
- Since Sheela and Divya together complete 5/8 units of work in 45 days, and Divya's work rate is 1/144 units per day, Sheela's work rate can be found by subtracting Divya's work rate from the combined work rate.
- Sheela's work rate is (5/8 - 1/144) / 45 = 1/72 units per day.
Step 6: Find the time taken by Sheela to complete the work alone
- Since Sheela's work rate is 1/72 units per day, to complete 1 unit of work, she will take 1 / (1/72) = 72 days.
Therefore, Sheela alone completes the work in 72 days. So, the correct answer is option (c) 72 days.
To make sure you are not studying endlessly, EduRev has designed Banking Exams study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Banking Exams.