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) 9 days
(b) 8 days
(c) 5 days
(d) 10 days
The correct answers to the above question in:
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
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Read more man leaves and joins Based Quantitative Aptitude Questions and Answers
Question : 1
A and B can do a piece of work in 12 days and 15 days respectively. They began to work together but A left after 4 days. In how many more days would B alone complete the remaining work ?
a) $25/3$ days
b) 6 days
c) 5 days
d) $20/3$ days
Answer »Answer: (b)
Part of the work done by A and B in 4 days
= $4(1/12 + 1/15) = 4({5 + 4}/60)$
= $4 × 9/60 = 3/5$
Remaining work = $1 - 3/5 = 2/5$
Time taken by B to complete the remaining work
= $2/5 × 15$ = 6 days
Using Rule 20,
Here, m = 12, n = 15, p = 4
B alone do the works in= ${mn - p(m + n)}/m$
= ${12 × 15 - 4(12 + 15)}/12$
= ${180 - 108}/12 = 72/12$ = 6 days
Question : 2
A and B together can complete a work in 12 days. A alone can complete in 20 days. If B does the work only half a day daily, then in how many days A and B together will complete the work ?
a) 20 days
b) 11 days
c) 15 days
d) 10 days
Answer »Answer: (c)
B’s 1 day's work
= $1/12 - 1/20 = {5 - 3}/60 = 1/30$
B's $1/2$ day’s work = $1/60$
(A + B)'s 1 day's work
= $1/20 + 1/60 = {3 + 1}/60 = 1/15$
[Since, B works for half day daily]
Hence, the work will be completed in 15 days.
Question : 3
A and B can separately complete a piece of work in 20 days and 30 days respectively. They worked together for some time, then B left the work. If A completed the rest of the work in 10 days, then B worked for
a) 8 days
b) 12 days
c) 16 days
d) 6 days
Answer »Answer: (d)
Let A and B worked together for x days
According to the question,
Part of work done by A for (x + 10) days
+ part of work done by B for x days = 1
${x + 10}/20 + x/30$ = 1
${3x + 30 + 2x}/60 = 1$
5x + 30 = 60
5x = 30 ⇒ x = $30/5$ = 6 days
Using Rule 20A can do a certain work in 'm' days and B can do the same work in 'n' days. They worked together for 'P' days and after this A left the work, then in how many days did B alone do the rest of work ?Required time = ${mn - P(m + n)}/m$ dayswhen after 'P' days B left the work, then in how many days did A alone do the rest of work?Required time = ${mn - P(m + n)}/n$ days
Here, m =20, n= 30, p = x and time taken by A alone = 10
10 = ${mn - p(m + n)}/n$
10 = ${30 × 20 - x(30 + 20)}/30$
300 = 600 - x 50
50x = 300 x = 6
B worked for 6 days
Question : 4
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 : 5
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 : 6
A and B can complete a piece of work in 12 and 18 days respectively. A begins to do the work and they work alternatively one at a time for one day each. The whole work will be completed in
a) 15$2/3$ days
b) 16$1/3$ days
c) 18$2/3$ days
d) 14$1/3$ days
Answer »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.
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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