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If A and B together can finish a certain work in ‘a’ days. They worked together for ‘b’ days and then ‘B’ (or A) left the work. A (or B) finished the rest of work in ‘d’ days, then, the total time taken by A (or B) alone to complete the work = ad / (a – b) or bd / (a – b) days

How did we derive this?
Most Upvoted Answer
If A and B together can finish a certain work in ‘a’ days. They worked...


Explanation of Derivation:

Given Information:
- A and B together can finish a work in 'a' days
- They worked together for 'b' days
- A finished the rest of the work in 'd' days
- Total time taken by A alone to complete the work = ad / (a - b) or bd / (a - b) days

Derivation Steps:

1. Let the total work be represented as 1 unit.
2. A and B together can finish the work in 'a' days, so their combined rate of work is 1/a.
3. They worked together for 'b' days, so the work completed in 'b' days is (b/a) units.
4. The remaining work to be completed by A alone is (1 - b/a) = ((a - b)/a) units.
5. A finishes the remaining work in 'd' days, so A's rate of work is 1/d.
6. Using the formula: Time = Work / Rate, we have Time taken by A alone = (1 - b/a) / 1/d = ((a - b)/a) * d = ad / a - b.
7. Similarly, the time taken by B alone can be calculated by substituting B's rate of work (1 - 1/a) and solving the equation, which results in bd / a - b days.

Therefore, the total time taken by A or B alone to complete the work is ad / (a - b) or bd / (a - b) days, as derived.
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If A and B together can finish a certain work in ‘a’ days. They worked together for ‘b’ days and then ‘B’ (or A) left the work. A (or B) finished the rest of work in ‘d’ days, then, the total time taken by A (or B) alone to complete the work = ad / (a – b) or bd / (a – b) daysHow did we derive this?
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If A and B together can finish a certain work in ‘a’ days. They worked together for ‘b’ days and then ‘B’ (or A) left the work. A (or B) finished the rest of work in ‘d’ days, then, the total time taken by A (or B) alone to complete the work = ad / (a – b) or bd / (a – b) daysHow did we derive this? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If A and B together can finish a certain work in ‘a’ days. They worked together for ‘b’ days and then ‘B’ (or A) left the work. A (or B) finished the rest of work in ‘d’ days, then, the total time taken by A (or B) alone to complete the work = ad / (a – b) or bd / (a – b) daysHow did we derive this? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B together can finish a certain work in ‘a’ days. They worked together for ‘b’ days and then ‘B’ (or A) left the work. A (or B) finished the rest of work in ‘d’ days, then, the total time taken by A (or B) alone to complete the work = ad / (a – b) or bd / (a – b) daysHow did we derive this?.
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