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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

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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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