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The following question based on time & work topic of quantitative aptitude
(a) 8$2/7$ days
(b) 5$5/7$ days
(c) 28 days
(d) 14 days
The correct answers to the above question in:
Answer: (b)
(A + B)’s 1 day’s work = $1/10$
(B + C)’s 1 day’s work = $1/6$
(C + A)’s 1 day’s work = $1/12$
Adding all three
2 (A + B + C)’s 1 day’s work = $1/10 + 1/6 + 1/12$
${6 + 10 + 5}/60 = 21/60 = 7/20$
(A + B + C)’s 1 day’s work = $7/40$
All three together will complete the work in $40/7 = 5{5}/7$ = days
Using Rule 5,
Time taken = ${2 × 10 × 6 × 12}/{10 × 6 + 6 × 12 + 12 × 10}$
= $1440/{60 + 72 + 120}$
= $1440/252 = 40/7 = 5{5}/7$ days
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Read more basics on time and work Based Quantitative Aptitude Questions and Answers
Question : 1
A, B and C together can complete a piece of work in 30 minutes. A and B together can complete the same work in 50 minutes. C alone can complete the work in
a) 150 minutes
b) 80 minutes
c) 60 minutes
d) 75 minutes
Answer »Answer: (d)
Work done by (A + B + C) in 1 minute = $1/30$
Work done by (A + B) in 1 minute = $1/50$
Work done by C alone in 1 minute = $1/30 - 1/50$
= ${5 - 3}/150 = 2/150 = 1/75$
C alone will complete the work in 75 minutes.
Using Rule 4,
C alone can do in = ${xy}/{x - y}$
= ${50 × 30}/{50 - 30}$ = 75 minutes
Question : 2
A can do a piece of work in 4 hours; B and C can do it in 3 hours. A and C can do it in 2 hours. How long will B alone take to do it ?
a) 24 hours
b) 8 hours
c) 10 hours
d) 12 hours
Answer »Answer: (b)
A’s 1 hour’s work = $1/4$
(B + C)’s 1 hour’s work = $1/3$
(A + C)’s 1 hour’s work = $1/2$
C’s 1 hour’s work
= $1/2 - 1/4 = {2 - 1}/4 = 1/4$
and B’s 1 hour’s work
= $1/3 - 1/4 = {4 - 3}/12 = 1/12$
Hence, B alone can do the work in 12 hours.
Question : 3
While working 7 hours a day, A alone can complete a piece of work in 6 days and B alone in 8 days. In what time would they complete it together, working 8 hours a day ?
a) 3.6 days
b) 2.5 days
c) 3 days
d) 4 days
Answer »Answer: (c)
A alone can complete the work in 42 days working 1 hour daily. Similarly, B will take 56 days working 1 hour daily.
A 's 1 day's work = $1/42$
B 's 1 day's work = $1/56$
(A + B) 's 1 day's work = $1/42 + 1/56 = {4 + 3}/168 = 7/168$
Time taken by (A + B) working 8 hours daily
= $168/{7 × 8}$ = 3 days
Using Rule 21If a man can do a certain work in '$d_1$' daysworking '$h_1$' hours in a days, while another man can do the same work in '$d_2$' days working '$h_2$' hours in a day. Whenthey work together everyday 'h' hours, then in how many days work will complete? Required time = $[{({h_1d_1}) × ({h_2d_2})}/{h_1d_1 + h_2d_2}] 1/h$
Here, $h_1$ = 7 hours, $h_2$ = 7 hours, $d_1$ = 6 days, $d_2$ = 8 days, h = 8 hours
Required Time = $[{({7 × 6}) × ({7 × 8})}/{7 × 6 + 7 × 8}] × 1/8$
= ${42 × 56}/98 × 1/8 = 2352/98 × 1/8 = 24/8$ = 3 days
Question : 4
A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work?
a) 3 days
b) 3.6 days
c) 7.5 days
d) 5.4 days
Answer »Answer: (b)
According to question,
A can finish the whole work in 6 days.
A’s one day’s work = $1/6$
Similarly, B’s one day’s work = $1/9$
(A + B)’s one day’s work
= $(1/6 + 1/9) = ({3 + 2}/18) = 5/18$
Therefore, (A + B)’s can finish the
whole work in $18/5$ days i.e., 3.6 days.
Using Rule 2If A completes a piece of work in 'x' days, and B completes the same work in 'y' days, then,Work done by A in 1 day = $1/x$, Work done by B in 1 day = $1/y$ Work done by A and B in 1 day = $1/x + 1/y = {x + y}/{xy}$Total time taken to complete the work by A and B both = $({xy}/{x + y})$
Time taken = ${6 × 9}/{9 + 6} = 54/15$ = 3.6 days
Question : 5
A and B together can complete a work in 8 days and B and C together in 12 days. All of the three together can complete the work in 6 days. In how much time will A and C together complete the work ?
a) 20 days
b) 12 days
c) 8 days
d) 10 days
Answer »Answer: (c)
Let A and C complete the work in x days
(A + B)’s 1 day’s work = $1/8$
(B + C)’s 1 day’s work = $1/12$
(C + A)’s 1 day’s work = $1/x$
Then (A + B + B + C + C + A)’s 1 day’s work = $1/8 + 1/12 + 1/x$
2(A + B + C)’s 1 day’s work = ${3x + 2x + 24}/{24x}$
(A + B + C)’s 1 day’s work = ${5x + 24}/{24x × 2}$
According to the question,
(A + B + C)’s 1 day’s work = $1/6$
$1/6 = {5x + 24}/{48x}$
30x + 144 = 48x ⇒ x = $144/18$ = 8 days.
Using Rule 5,
Let the time taken by A and C bc x days
Total time taken = ${2 × 8 × 12 × x}/{8 × 12 + 12 × x + 8 × x}$
6 = ${192x}/{96 +20x}$
576 + 120x = 192x
72x = 576 ⇒ x = 8
Time taken by A and C is 8 days.
Question : 6
A and B together can do a work in 8 days, B and C together in 6 days while C and A together in 10 days, if they all work together, the work will be completed in :
a) 4$4/9$ days
b) 5$5/47$ days
c) 3$3/4$ days
d) 3$3/7$ days
Answer »Answer: (b)
(A + B)'s 1 day's work = $1/8$ ...(i)
(B + C)'s 1 day's work = $1/6$ ...(ii)
(C + A)'s 1 day's work = $1/10$ ...(iii)
On adding,
2(A + B + C)'s 1 day's work = $1/8 + 1/6 + 1/10$
= ${15 + 20 + 12}/120 = 47/120$
(A + B + C)'s 1 day’s work= $47/240$
(A + B + C) together will complete the work in
$240/47 = 5{5}/47$ days.
Using Rule 5,
Time taken = ${2 × 8 × 6 × 10}/{8 × 6 + 6 × 10 + 10 × 8}$
= $960/{48 + 60 + 80} = 960/188$
= $240/47 = 5{5}/47$ days
time & work Shortcuts and Techniques with Examples
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Model 1 Basics on Time & Work
Defination & Shortcuts … -
Model 2 Formula method ‘M1D1W1 = M2D2W2’
Defination & Shortcuts … -
Model 3 Man leaves & joins
Defination & Shortcuts … -
Model 4 Working with Man, Woman, Child
Defination & Shortcuts … -
Model 5 Split & Fraction of work
Defination & Shortcuts … -
Model 6 Efficiency of the worker
Defination & Shortcuts … -
Model 7 Working with individual wages
Defination & Shortcuts …
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