Model 3 Man leaves & joins Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on time & work topic of quantitative aptitude
(a) 15$2/3$ days
(b) 16$1/3$ days
(c) 18$2/3$ days
(d) 14$1/3$ days
The correct answers to the above question in:
Answer: (d)
A’s 1 day’s work = $1/12$
B’s 1 day’s work = $1/18$
Part of work done by A and B in first two days
= $1/12 + 1/18 = {3 - 2}/36 = 5/36$
Part of work done by A and B in 14 days = $35/36$
[14 days to be taken randomly]
Remaining work = $1 - 35/36 = 1/36$
Now A will work for 15th day.
A will do the $1/36$ work in $1/36 × 12 = 1/3$ day.
Total Work will be done in $14{1}/3$ days.
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Read more man leaves and joins Based Quantitative Aptitude Questions and Answers
Question : 1
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 ?
a) 60 days
b) 48 days
c) 54 days
d) 50 days
Answer »Answer: (a)
(A+B)’s 1 day’s work = $1/30$
(A + B)’s 20 day’s work = $20/30 = 2/3$
Remaining work = $1 - 2/3 = 1/3$
Now, $1/3$ part of work is done by A in 20 days.
Whole work will be done by A alone in 20 × 3 = 60 days.
Question : 2
A, B and C can complete a work in 10, 12 and 15 days respectively. They started the work together. But A left the work before 5 days of its completion. B also left the work 2 days after A left. In how many days was the work completed?
a) 5 days
b) 7 days
c) 8 days
d) 4 days
Answer »Answer: (b)
Let the work be completed in x days.
According to the question,
${x - 5}/10 + {x - 3}/12 + x/15$ = 1
${6x - 30 + 5x - 15 + 4x}/60$ = 1
15x - 45 = 60
15x = 105 ⇒ x = $105/15$ = 7
Hence, the work will be completed in 7 days.
Question : 3
A and B can do a work in 45 days and 40 days respectively. They began the work together but A left after some time and B completed the remaining work in 23 days. After how many days of the start of the work did A leave ?
a) 9 days
b) 8 days
c) 5 days
d) 10 days
Answer »Answer: (a)
(A + B)’s 1 day’s work
= $(1/45 + 1/40) = {8 + 9}/360 = 17/360$
Work done by B in 23 days
= $1/40 × 23 = 23/40$
Remaining work = $1 - 23/40 = 17/40$
Now, $17/360$ work was done by (A + B) in 1 day
$17/40$ work was done by (A + B) in $1 × 360/17 × 17/40$ = 9 days.
Hence, A left after 9 days.
Using Rule 26A and B can do a piece of work in x and y days, respectively. Both begin together but after some days.A leaves the job and B completed the remaining work in a days. After how many days did A leave?Required time, t = $\text"(y - a)"/\text"(x + y)" × x$
Here, x = 45, y = 40, a = 23
Required time t= $\text"(y - a)"/\text"(x + y)" × x$
t = ${(40 - 23) × 45}/{45 + 40} = {17 × 45}/85$
t = 9 days
Question : 4
A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in :
a) 6 days
b) 10 days
c) 10$1/2$ days
d) 5 days
Answer »Answer: (b)
Work done by (B + C) in 3 days.
= $3 × (1/9 + 1/12)$
= $1/3 + 1/4 = {4 + 3}/12 = 7/12$
Remaining work = $1 - 7/12 = 5/12$
This part of work is done by A alone.
Now, $1/24$ part of work is done by A in 1 day.
∴ $5/12$ part of work will be done by A in
= $24 × 5/12$ = 10 days.
Question : 5
A and B alone can complete work in 9 days and18 days respectively. They worked together; however 3 days before the completion of the work A left. In how many days was the work completed ?
a) 8 days
b) 6 days
c) 5 days
d) 13 days
Answer »Answer: (a)
Let the work be completed in x days.
According to the question,
A worked for (x –3) days, while B worked for x days.
${x - 3}/9 +x/18$ = 1
${2x - 6 + x}/18$ = 1
3x–6 = 18
3x = 18 + 6 = 24 ⇒ x = $24/3$ = 8 days
Using Rule 8,
Here, x = 9, y = 18, m = 3
Total time taken = ${(x + m)y}/{x + y}$
=${(9 + 3) × 18}/{9 + 18}$
= ${12 × 18}/27$ = 8 days
Question : 6
A can do a piece of work in 20 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in
a) 7 days
b) 11 days
c) 3 days
d) 5 days
Answer »Answer: (d)
Work done by B in 9 days = $9/12 = 3/4$ part
Remaining work
= $1 - 3/4 = 1/4$ which is done by A
Time taken by A = $1/4 × 20$ = 5 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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