Time and work Quantitative aptitude question

[Q] A and B working together can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B leaves and A alone completes the remaining work. The whole work was completed in how many days?
(a) 16 days
(b) 18 days
(c) 14 days
(d) 12 days

Solution

Answer   (d)
Explanation
----
Work done by A in 1 day = 1/15

Work done by B in 1 day = 1/10



Work done by A and B in 1 day = 1/15 + 1/10 = 1/6

Work done by A and B in 2 days = 2 × (1/6) = 1/3

Remaining work = 1 – 1/3 = 2/3



Time taken by A to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days

Total time taken = 2 + 10 = 12 days

Time and work Quantitative aptitude question

[Q] A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B leaves and A alone and completes the remaining work. Then,the whole work was completed in how many days?
(a) 14 days
(b) 12 days
(c) 13 days
(d) 11 days

Solution

Answer   (b)
Explanation
----
Work done by A in 1 day = 1/15

Work done by B in 1 day = 1/10



Work done by A and B in 1 day = 1/15 + 1/10 = 1/6

Work done by A and B in 2 days = 2 × (1/6) = 1/3

Remaining work = 1 – 1/3 = 2/3



Time taken by A to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days

Total time taken = 2 + 10 = 12 days

Time and work Quantitative aptitude question

[Q] X takes twice as much time as Y or thrice as much time as Z to finish a piece of work. If Working together, they can finish the work in 2 days. Then, working alone, how many days will Y take to complete the work?
(a) 5 days
(b) 6 days
(c) 4 days
(d) 7 days

Solution

Answer   (b)
Explanation
----
Let X takes x days to complete the work,

Then Y takes x/2 days and Z takes x/3 days to complete the work

Amount of work X does in 1 day = 1/x

Amount of work Y does in 1 day = 2/x

Amount of work Z does in 1 day = 3/x

Amount of work X,Y and Z do in 1 day = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x

6/x = 2

=> x = 12

=> Y takes 12/2 days = 6 days to complete the work

Time and work Quantitative aptitude question

[Q] A and B are working on an assignment. A takes 6 hours to type 32 pages on a computer, while B takes 5 hours to type 40 pages. How much time will A and B take, working together on two different computers to type an assignment of 110 pages?
(a) 10 hour 15 minutes
(b) 7 hour 15 minutes
(c) 8 hour 15 minutes
(d) 9 hour 15 minutes

Solution

Answer   (c)
Explanation
----
Pages typed by A in 1 hour = 32/6 = 16/3

Pages typed by B in 1 hour = 40/5 = 8

Pages typed by A and B in 1 hour = 16/3 + 8 = 40/3

Time taken to type 110 pages when A and B work together = 110 × 3 /40 = 33/4

= 8 ¼ hours = 8 hour 15 minutes

Time and work Quantitative aptitude question

[Q] A can do a piece of work in 20 days. B is 25% more efficient than A. The number of days taken by B to do the same piece of work is?

(a) 14 days
(b) 15 days
(c) 16 days
(d) 13 days

Solution

Answer   (c)
Explanation
----
Work done by A in 1 day = 1/20

Work done by B in 1 day = (1/20) × (125/100) = 5/80 = 1/16

=> B can complete the work in 16 days

Time and work Quantitative aptitude question

[Q] If A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Then, working together, they will complete the same work in how many days?
(a) 3 ³⁄₇
(b) 2 ³⁄₇
(c) 5 ³⁄₇
(d) 4 ³⁄₇

Solution

Answer   (a)
Explanation
----
Work done by A in 1 day = 1/24

Work done by B in 1 day = 1/6

Work done by C in 1 day = 1/12

Work done by A,B and C in 1 day = 1/24 + 1/6 + 1/12 = 7/24

=> Working together, they will complete the work in 24/7 days = 3 ³⁄₇ days

Time and work Quantitative aptitude question

[Q] If A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
(a) 23 days
(b) 13 days
(c) 33 days
(d) 43 days

Solution

Answer   (b)
Explanation
----
Work done by A in 1 day = 1/23

Let work done by B in 1 day = b

b × (130/100) = 1/23

=> b = 100/(23×130) = 10/(23×13)

Work done by A and B in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13

=> A and B together can do the work in 13 days

Time and work Quantitative aptitude question

[Q] A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
(a) 4
(b) 2
(c) 5
(d) 6

Solution

Answer   (d)
Explanation
----
Work done by A in 1 day = 1/18

Work done by B in 1 day = 1/15

Work done by B in 10 days = 10/15 = 2/3

Remaining work = 1 – 2/3 = 1/3

Number of days in which A can finish the remaining work = (1/3) / (1/18) = 6

Time and work Quantitative aptitude question

[Q] 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
(a) 60 days
(b) 40 days
(c) 50 days
(d) 30 days

Solution

Answer   (b)
Explanation
----

Work done by 4 men and 6 women in 1 day = 1/8

Work done by 3 men and 7 women in 1 day = 1/10

Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as

4m + 6w = 1/8 ---(1)

3m + 7w = 1/10 ---(2)

Solving equation (1) and (2) , we get m=11/400 and w=1/400

Amount of work 10 women can do in a day = 10 × (1/400) = 1/40

Ie, 10 women can complete the work in 40 days

Time and work Quantitative aptitude question

[Q] A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?
(a) 4 pm
(b) 3 pm
(c) 2 pm
(d) 1 pm

Solution

Answer   (d)
Explanation
----
Work done by P in 1 hour = 1/8

Work done by Q in 1 hour = 1/10

Work done by R in 1 hour = 1/12

Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120

Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60



From 9 am to 11 am, all the machines were operating.

Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60



Pending work = 1- 37/60 = 23/60

Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11

which is approximately equal to 2

Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm

Time and work Quantitative aptitude question

[Q] 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.
(a) 5 days
(b) 2 days
(c) 4 days
(d) 6 days

Solution

Answer   (c)
Explanation
----
Let work done by 1 man in 1 day = m,
work done by 1 woman in 1 day = w

Work done by 6 men and 8 women in 1 day = 1/10

=> 6m + 8w = 1/10

=> 60m + 80w = 1 ------ (1)

Work done by 26 men and 48 women in 1 day = 1/2

=> 26m + 48w = ½

=> 52m + 96w = 1 ------  (2)

Solving equation 1 and equation 2. We get m = 1/100 and w = 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

Time and work Quantitative aptitude question

[Q] A alone can do a piece of work in 6 days and B alone can do it in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
(a) 400
(b) 200
(c) 300
(d) 100

Solution

Answer   (a)
Explanation
----
Amount of work A can do in 1 day = 1/6

Amount of work B can do in 1 day = 1/8

Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24

Amount of work A + B + C can do = 1/3

Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24

work A can do in 1 day: work B can do in 1 day: work C can do in 1 day

= 1/6 : 1/8 : 1/24 = 4 : 3 : 1

Amount to be paid to C = 3200 × (1/8) = 400

Time and work Quantitative aptitude question

[Q] P is thrice as good as workman as Q and therefore is able to finish a job in 60 days less than Q. Working together, they can do it in:
(a) 20 ½ days
(b) 22 ½ days
(c) 21 ½ days
(d) 23 ½ days

Solution

Answer   (b)
Explanation
----
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

Time and work Quantitative aptitude question

[Q] A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
(a) 45 days
(b) 15 days
(c) 30 days
(d) 25 days

Solution

Answer   (b)
Explanation
----
Amount of work A can do in 1 day = 1/20

Amount of work B can do in 1 day = 1/30

Amount of work C can do in 1 day = 1/60

A is working alone and every third day B and C is helping him

Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5

So work completed in 15 days = 5 × 1/5 = 1

Ie, the work will be done in 15 days

Time and work Quantitative aptitude question

[Q] A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in how much days?
(a) 9 (1/5) days
(b) 9 (3/5) days
(c) 9 (2/5) days
(d) 9 (4/5) days

Solution

Answer   (b)
Explanation
----

Amount of work A can do in 1 day = 1/16

Amount of work B can do in 1 day = 1/12

Amount of work A, B and C can together do in 1 day = 1/4

Amount of work C can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48

=> Hence C can do the job on 48/5 days = 9 (3/5) days

Time and work Quantitative aptitude question

[Q] A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, Find the fraction of the work that is left

(a) 15/8
(b) 8/15
(c) 17/8
(d) 8/17

Solution

Answer   (b)
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