Question 1

What is the verified answer to “Solve this Time and Work question: A and B together finish a job in 18 days, B and C in 30 days, and C and A in 45 days. In how many days will A, B, and C together finish it?”?

Accepted Answer

18 days, option A.

Question 2

Which method solves this Time and Work item?

Accepted Answer

Rebuild and verify the complete work-rate equation.

Question 3

Why are the other options incorrect?

Accepted Answer

17 days, 19 days, 20 days break a clue, direction, transition or operation.

Question 4

How should the answer be checked?

Accepted Answer

Replay the rule from the first clue or term and test every intermediate step.

Question 5

What is Time and Work and what is the basic concept?

Accepted Answer

Time and Work problems involve finding how long it takes to complete a task. Basic concept: If A can do a work in n days, A's one day work = 1/n. If A and B together can do work in n days, combined one day work = 1/n. Key formula: Total Work = Efficiency x Time. Time and Work is a major topic in SSC CGL, IBPS Bank PO, SBI PO, CAT, and Railway exams.

Question 6

How to solve Time and Work problems using LCM method?

Accepted Answer

LCM Method: Assume total work = LCM of given days. Calculate each person's work per day = Total work divided by Days. Combined work per day = Sum of individual work rates. Time = Total work divided by Combined rate. Example: A can do work in 10 days, B in 15 days. LCM(10,15) = 30 units. A's daily work = 3 units, B's = 2 units. Together = 5 units/day. Time = 30/5 = 6 days. This avoids fractions and is much faster.

Question 7

How to solve problems when people join or leave work midway?

Accepted Answer

When worker joins midway: Find work done before and after they join. If A works for x days and B joins for y days, Total work = A's work in x days + (A+B)'s work in y days. Example: A alone in 20 days. If A works 6 days then B joins, to find when work completes: A's 6 days work = 6/20 = 3/10. Remaining = 7/10. If A+B together rate = 1/12, days to finish = (7/10)/(1/12) = 8.4 days.

Question 8

What are Pipes and Cistern problems in Time and Work?

Accepted Answer

Pipes and Cistern: Inlet pipe fills cistern (positive), Outlet pipe empties cistern (negative). If inlet fills in x hours, rate = 1/x per hour. If outlet empties in y hours, rate = 1/y per hour. Net rate = 1/x - 1/y. Time to fill = xy/(y-x) hours if y > x. Cistern fills if net rate is positive. These problems are standard in IBPS, SBI, and SSC competitive exams.

Question 9

What is work equivalence and efficiency in Time and Work problems?

Accepted Answer

Work Equivalence: Men x Days = Women x Days (when efficiency ratio is known). If 1 man = 2 women in efficiency, then 10 men = 20 women. Men-Days concept: 10 men x 5 days = 50 man-days. If 8 men do same work, days = 50/8 = 6.25 days. For wages: divide total payment in ratio of work done. If A and B complete work together and A worked fewer days, calculate individual shares accordingly.

Solve this Time and Work question: A and B together finish a job in 18 days, B and C in 30 days, and C and A in 45 days. In how many days will A, B, and C together finish it?

Explanation

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