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) 18 days
(b) 16 days
(c) 20 days
(d) 15 days
The correct answers to the above question in:
Answer: (b)
Time taken by A
= ${8 × 12}/128 = {8 × 12}/4 = 24$ days
Work done of by B = $4/12 = 1/3$
Remaining work = $1 - 1/3 = 2/3$
Since, A can complete a work in 24 days
A can complete $2/3$ part of work in 24 × $2/3$ = 16 days
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Read more man leaves and joins Based Quantitative Aptitude Questions and Answers
Question : 1
A can do a piece of work in 12 days and B can do it in 18 days. They work together for 2 days and then A leaves. How long will B take to finish the remaining work ?
a) 8 days
b) 10 days
c) 13 days
d) 6 days
Answer »Answer: (c)
(A+B)’s 2 days’ work = $2(1/12 + 1/18) = 10/36$
Remaining work = $1 - 10/36 = 26/36$
Time taken by B to complete $26/36$ part of work
= $26/36$ × 18 = 13 days
Using Rule 20,
Here, m = 12, n = 18, p = 2
Time taken by B = $\text"mn - p(m+n)"/ \text"m"$
= ${12 × 18 - 2(12 + 18)}/12$
= ${216 - 60}/12$ = 13 days
Question : 2
A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately with A beginning, the work would be completed in
a) 10$1/2$ days
b) 10$1/4$ days
c) 10$1/3$ days
d) 10$2/3$ days
Answer »Answer: (b)
Part of work done by A and B in first two days
= $1/9 + 1/12 = {4 - 3}/36 = 7/36$
Part of work done in first 10 days = $35/36$
Remaining work = $1 - 35/36 = 1/36$
Now it is the turn of A.
Time taken by A
= $1/36 × 9 = 1/4$ day
Total time = $10 + 1/4 = 10{1}/4$ days
Question : 3
A and B can do a job in 6 and 12 days respectively. They began the work together but A leaves after 3 days. Then the total number of days needed for the completion of the work is :
a) 5 days
b) 6 days
c) 9 days
d) 4 days
Answer »Answer: (b)
A’s one day’s work = $1/6$
B’s one day’s work = $1/12$
(A + B)’s one day’s work = $1/6 + 1/12 = {2 + 1}/12 = 1/4$
(A + B)’s three day’s work = $3/4$
Remaining work = $1 - 3/4 = 1/4$
Total required number of days
= $1/4 × 12/1 + 3$ = 3 + 3 = 6 days
Using Rule 20,
Here, m = 6, n= 12, and p = 3
Time taken by B = $\text"mn - p(m+n)"/ \text"m"$
= ${6 × 12 - (6 + 12) × 3}/6 = {72 - 54}/6$ = 3 days
Total number of days taken to finish the works = 6 days
Question : 4
A certain number of persons can complete a piece of work in 55 days. If there were 6 persons more, the work could be finished in 11 days less. How many persons were originally there ?
a) 24
b) 30
c) 22
d) 17
Answer »Answer: (a)
Originally, let there be x men
Now, more men, less days
(x + 6) : x : : 55 : 44
So, ${x + 6}/x = 55/44 = 5/4$
or 5x = 4x + 24 ⇒ x = 24
Using Rule 23Some people finish a certain work in 'D' days. If there were 'a' less people, then the work would be completed in 'd'days more, what was the number of people initially?Required number = $\text"a(D - d)"/\text"d"$ people
Here, D = 55, a = 6, d = 11
No of people initially = $\text"a(D - d)"/\text"d"$
= ${6(55 - 11)}/11$ = 24
Question : 5
A can complete a piece of work in 18 days, B in 20 days and C in 30 days. B and C together start the work and are forced to leave after 2 days. The time taken by A alone to complete the remaining work is
a) 12 days
b) 15 days
c) 16 days
d) 10 days
Answer »Answer: (b)
(B + C)’s 2 days’ work = $2(1/20 + 1/30)$
= $2({3 + 2}/60) = 1/6$ part
Remaining work = $1 - 1/6 = 5/6$ part
Time taken by A to complete this part of work
= $5/6$ × 18 = 15 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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