 # Aptitude - Aptitude-Time And Works

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A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes in 13 days. In how many days C alone will do the work?

• • • • a
• b
• c
• d

(A + B)s 5 days work + (B + C)s 2 days work + Cs 11 days work = 1.
5/12 + 6/12 + Cs 11 days work = 11/24
Cs 1 days work = (11/24) * (1/11) = 1/24
C alone can finish it in 24 days.

If Ramesh, Suresh and Harish can do a piece of work in 15 days, 10 days and 6 days respectiVelY how long will they take to do it, if all the three work at it together ?

• • • • a
• b
• c
• d

A and B can dO a Piece of work in 5 days ;B and c can do it in 7 day; A and C can do it in 4 days. Who among these will take the least time if put to do it alone ?

• • • • a
• b
• c
• d

(A+B)s 1 days work = 1/4
and (A+C)’s 1 day’s work = 1/4
2(A+B+C)s 1 days work = (1/5 + 1/7 + 1/4) = 83/140
(A+B+C)s 1 days work = 83/280
Cs 1 days work = (83/280 - 1/5) = 27/280
As 1 days work = (83/280 - 1/7) = 43/280
Bs 1 days work = (83/280 - 1/4) = 13/280
Thus time taken by A, B, C is 280/43 days, 280/13 days, 280/27 days respectively.
Clearly, the time taken by A is least.

A and B can separately do a piece of work in 20 and 15 days respectively. They worked together for 6 days, after which B was replaced by C. If the work was finished in next 4 days, then the number of days in which C alone could do the work will be ?

• • • • a
• b
• c
• d

(A + B)s 6 days work = 6 [(1/20) + (1/15)] = 7/20
(A+C)s 4days work = (3/10)*(A+C)s 1days work = 1/20 Cs 1 days work = (3/40) - (1/20) = 1/40
Hence, C alone can finish the work in 40 days.

45 men can complete a work in 16 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work ?

• • • • a
• b
• c
• d