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# Arithmetic Aptitude :: Time and Work

Home > Arithmetic Aptitude > Time and Work > General Questions

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1. A' and 'B' complete a work togather in 8 days.If 'A' alone can do it in 12 days.Then how many day 'B' will take to complete the work?

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Explanation:

A & B one day work = 1/8
A alone one day work = 1/12
B alone one day work = (1/8 - 1/12) = ( 3/24 - 2/24)
=> B one day work = 1/24
so B can complete the work in 24 days.

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2. If A alone can do a piece of work in 8 days and B alone can do the same work in 12 days. How many days A and B required to finish the same work if they work togather?

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Explanation:

A alone one day work = 1/8
B alone one day work = 1/12
Both A and B one day work = (1/8 + 1/12) = (3/24 + 2/24)
= 5/24
so A and B together finish the work in 24/5 day
or 4 4/5 days.

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3. A can finish a piece work in 18 days and B can do the same work in half the time taken by A. So if they working together, what part of the same work can finished in a day?

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Explanation:

First find the 1 day work of both (A & B)
A's 1 day's work = 1/18
and
B's 1 day's work = 1/9 (B can do work in half time)
(A + B)'s 1 day's work = (1/18+1/9)
= (1+2)/18 = 3/18 = 1/6
so A & B together can do 1/6 of work in 1 day.

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4. A can do a work in 10 days and B can do the same work in 15 days. So how many days they will take to finish the same work ?

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Explanation:

First find the 1 day work of both (A & B)
A 1 day's work = 1/10
and
B 1 day's work = 1/15

So (A + B) 1 day's work = (1/10+1/15)
= (3/30+2/30) = 5/30 = 1/6

So Both (A & B) together can finish work in 6 days

Workspace

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5. P, Q and R are three typists who working simultaneously can type 216 pages in 4 hours. In one hour, R can type as many pages more than Q as Q can type more than P. During a period of five hours, R can type as many pages as P can during seven hours. How many pages does each of them type per hour ?

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Explanation:

Let's the number of pages typed in one hour by P, Q and R be p, q and r respectively. Then,

P,Q and R typed page in 1 hrs = 216/4
=> p + q + r = 216/4
=> p + q + r = 54 ...(i)

r - q = q - p => 2p = q + r ...(ii)

5r = 7p => p = 5/7 r ...(iii)

By Solving above (i), (ii) and (iii) equations
=> p = 15, q = 18, q = 21

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6. X can do 1/4 of a work in 10 days, Y can do 40% of the work in 40 days and Z can do 1/3 of the work in 13 days. Who will complete the work first ?

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Explanation:

x can do 1/4 of work in = 10 days
so x can do whole work in = (10 x 4) = 40 days.

Y can do (40% or 40/100)of work in = 40 days
so Whole work can be done by Y = (40x100/40)= 100 days.

Z can do 1/3 of work in = 13 days
Whole work will be done by Z in (13 x 3) = 39 days.

so compare x , y ,z work compare = y > x > z
so Z can complete the work first.

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7. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last ?

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Explanation:

X one day work = 1/20

y one day work = 1/12

work done by x in 4 days = 4 * 1/20 = 1/5
left work = (1-1/5) = 4/5

x and y one day work = (1/20 + 1/12) = 8/60 = 2/15
=> time required to do 2/15 part of work by x and y = 1 day
so for whole work = 1/(2/15) = 15/2
so for 4/5 part of work x and y will take =( 4/5*15/2 ) = 6 days.
=> How long did the work last = 4 day + 6 day = 10 days.

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8. A and B can together finish a work in 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the job ?

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Explanation:

(A + B)'s 1 day's work = 1/30

so (A&B) 20 days work = (20*1/30) = 2/3

so left work = (1?2/3)=1/3

1/3 work is done by A = 20 days.

So whole work will be done by A = (20 x 3) = 60 days.

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9. A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work ?

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Explanation:

(A & B)'s 1 day work = 1/30
(B & C)'s 1 day work = 1/24
(C & A)'s 1 day work = 1/20

so 2 (A + B + C)'s 1 day's work = (1/30+1/24+1/20) = 15/120 = 1/8

=> (A + B + C)'s 1 day's work = 1/16

Work done by A, B and C in 10 days = (10*1/16) = 5/8
so left work = (1?5/8)=3/8

A's 1 day's work (1/16?1/24)=1/48

=> 1/48 part of work is done by A = 1 day.

So, 3/8 part of work will be done by A = (48?3/8) = 6*3 = 18 days.

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10. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone ?

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Explanation:

A's 1 day's work = x
and B's 1 day's work = y
So (A & B) 1 day work = 1/30 => x+y =1/30
=> 30x + 30y = 1 -------- (1)

So 16x + 44y = 1 -------- (2)

By Solving above two equations,
x = 1/60 and y = 1/60

B's 1 day's work = 1/60

Hence, B alone shall finish the whole work in 60 days.

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Time and work are one of the most important topics of quantitative aptitude written exams. You can browse this page to find the time and work quantitative aptitude questions and start practicing right now.

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