# TIME AND WORK

 1. A is able to do a piece of work in 15 days and B can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left? Ans- 8/15  EXPLANATION –  Amount of work A can do in 1 day = 1/15 Amount of work B can do in 1 day = 1/20 Amount of work A and B can do in 1 day = 1/15 + 1/20 = 7/60 Amount of work A and B can together do in 4 days = 4 × (7/60) = 7/15 Fraction of work left = 1 – 7/15= 8/15 Q  2- P is thrice as good as Q in work. P is able to finish a job in 60 days less than Q. They can finish the work in – days if they work together. ANS-  22 ½ days EXPLANANTION If P  completes a work in 1 day, Q completes the same work in 3 days Hence, if the difference is 2 days, Q can complete the work in 3 days => if the difference is 60 days, Q can complete the work in 90 days => Amount of work Q  can do in 1 day= 1/90 Amount of work P can do in 1 day = 3 × (1/90) = 1/30 Amount of work P and Q can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45 => P and Q together can do the work in 45/2 days = 22 ½ days Q 3-  6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in – days. ANS- 4 days EXPLANANTION Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b Work done by 6 men and 8 women in 1 day = 1/10 => 6m + 8b = 1/10 => 60m + 80b = 1 — (1) Work done by 26 men and 48 women in 1 day = 1/2 => 26m + 48b = ½ => 52m + 96b = 1— (2) Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200 Work done by 15 men and 20 women in 1 day = 15/100 + 20/200 =1/4 => Time taken by 15 men and 20 women in doing the work = 4 days Q6-  A can do a work in the same time in which B and C together can do it. If A and B work together, the work can be completed in 10 days. C  alone needs 50 days to complete the same work. then B alone can do it in ANS- 25 DAYS EXPLANANTION Work done by A and B in 1 day = 1/10 Work done by C in 1 day = 1/50 Work done by A, B and C in 1 day = 1/10 + 1/50 = 6/50 But Work done by A in 1 day = Work done by B and C in 1 day . Hence the above equation can be written as Work done by A in 1 day × 2 = 6/50 => Work done by A in 1 day = 3/50 => Work done by B and C in 1 day = 3/50 Hence work done by B in 1 day = 3/50 – 1/50 = 2/50 = 1/25 So B alone can do the work in 25 days
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