A takes twice as long as B to finish a job, and C takes three times as long as B. Working together, they finish the job in 12 days. How many days would A take to do the job alone?
Aptitude
Time and Work
Difficulty: Easy
Choose an option
Answer
Correct Answer: 44
Explanation
Introduction / Context:Express all times relative to B. Convert to rates, add to get the joint rate, equate to the given joint time, and back out A’s time.
Given Data / Assumptions:
- A = 2B, C = 3B (in time).
- Together time = 12 days.
Concept / Approach:If B needs t days, then rates are: A = 1/(2t), B = 1/t, C = 1/(3t). Sum to get 11/(6t). Set 12 * 11/(6t) = 1 to solve for t and then 2t.
Step-by-Step Solution:
Joint rate = 1/(2t) + 1/t + 1/(3t) = 11/(6t)12 * (11/(6t)) = 1 → 22/t = 1 → t = 22A alone time = 2t = 44 daysVerification / Alternative check:Compute joint rate with t=22: 1/44 + 1/22 + 1/66 = 1/12 → consistent.
Why Other Options Are Wrong:They correspond to incorrect algebra when resolving t or doubling to get A’s time.
Common Pitfalls:Adding times rather than rates; mixing up “takes twice the time” with “twice as efficient.”
Final Answer:44