Model 3 Man leaves & joins Practice Questions Answers Test with Solutions & More Shortcuts
time & work PRACTICE TEST [7 - EXERCISES]
Model 1 Basics on Time & Work
Model 2 Formula method ‘M1D1W1 = M2D2W2’
Model 3 Man leaves & joins
Model 4 Working with Man, Woman, Child
Model 5 Split & Fraction of work
Model 6 Efficiency of the worker
Model 7 Working with individual wages
Question : 21 [SSC CGL Prelim 2003]
8 men can do a work in 12 days. After 6 days of work, 4 more men were engaged to finish the work. In how many days would the remaining work be completed?
a) 3
b) 4
c) 5
d) 2
Answer »Answer: (b)
Using Rule 1If $M_1$ men can finish $W_1$ work in $D_1$ days and $M_2$ men can finish $W_2$ work in $D_2$ days then, Relation is${M_1D_1}/{W_1} = {M_2D_2}/{W_2}$ andIf $M_1$ men finish $W_1$ work in $D_1$ days, working $T_1$ time each day and $M_2$ men finish $W_2$ work in $D_2$ days, working $T_2$ time each day, then${M_1D_1T_1}/{W_1} = {M_2D_2T_2}/{W_2}$
Work done by 8 men in 6 days
= $6/12 = 1/2$
Remaining work
= $1 - 1/2 = 1/2$
4 more men are engaged.
Total number of men = 8 + 4 = 12
By work and time formula
$W_1/{M_1D_1} = W_2/{M_2D_2}$, we have
$1/{8 × 12} = {1/2}/{12 × D_2}$
$D_2 = 1/2 × {8 × 12}/12$ = 4 days.
Question : 22 [SSC CGL Prelim 2008]
40 men can complete a work in 40 days. They started the work together. But at the end of each 10th day, 5 men left the job. The work would have been completed in
a) 53$1/3$ days
b) 52 days
c) 50 days
d) 56 $2/3$ days
Answer »Answer: (d)
For the first 10 days 40 men worked.
Now, 40 men can complete the work in 40 days
1 man will complete the same work in 1600 days
1 man’s 1 day’s work = $1/1600$
Part of work done in first 10 days = $1/4$
For the next 10 days 35 men worked.
Part of the work done
= ${1 × 35 × 10}/1600 = 7/32$
For the next 10 days, 30 men worked
Part of the work done
= ${30 × 10}/1600 = 3/16$
For the next 10 days, 25 men worked. Part of the workdone
= ${25 × 10}/1600 = 5/32$
Similarly, part of the work done by 20 men in next 10 days
= ${20 × 10}/1600 = 1/8$
Work done in 50 days
= $1/4 + 7/32 + 3/16 + 5/32 + 1/8$
= ${8 + 7 + 6 + 5 + 4}/32 = 30/32 = 15/16$
Remaining work = $1 - 15/16 = 1/16$
Now 15 men remain to work
15 men’s 1 day’s work= $15/1600$
Time taken to complete $1/16$ part of work
= $1600/15 × 1/16 = 20/3 = 6{2}/3$ days
Total time = $50 + 6{2}/3 = 56{2}/3$ days
Question : 23 [SSC CPO S.I.2003]
A and B can do a piece of work in 28 and 35 days respectively. They began to work together but A leaves after sometime and B completed remaining work in 17 days. After how many days did A leave ?
a) 9 days
b) 8 days
c) 7$5/9$ days
d) 14$2/5$ days
Answer »Answer: (b)
Let A worked for x days.
According to question
$x/28 + (x + 17)/35 = 1$
${5x + 4(x + 17)}/140 = 1$
5x + 4x + 68 = 140
9x = 140 - 68 = 72
x = 8
∴ A worked for 8 days
Question : 24 [SSC SO 2005]
A man and a boy can complete a work together in 24 days. If for the last six days man alone does the work then it is completed in 26 days. How long the boy will take to complete the work alone ?
a) 20 days
b) 24 days
c) 36 days
d) 72 days
Answer »Answer: (d)
Suppose a man can complete the work in x days and that boys in y days.
According to question
$24/x + 24/y$ = 1 … (i) × 13
$26/x + 20/y = 1$ … (ii) × 12
$312/x + 312/y = 13$
$312/x + 240/y = 12$
Solving these two equations we get,
$72/y$ = 1 ⇒ y = 72 days
Boys alone can complete the work in 72 days
Using Rule 9If A and B together can finish a certain work in 'a' days. They worked together for 'b' days and then 'B'(or A) left the work. A (or B) finished the rest work in 'd' days, thenTotal time taken by A (or B) alone to complete the work= $\text"ad"/ \text"a - b"$ or $\text"bd"/ \text"a - b"$ days
Here, a = 24, b = 24 - 6 = 18, d = 26 days
Total time taken by B alone to complete the work
= $\text"bd"/ \text"a - b"- 6$
(Since, man has work d or 6 days)
= ${18 × 26}/{24 - 18} - 6$ = 78 - 6 = 72 days
Question : 25 [SSC CGL Tier-I 2010]
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
IMPORTANT quantitative aptitude EXERCISES
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Top 199+ Time and Work Efficiency Based Aptitude MCQ Quiz »
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New 299+ Time and Work Aptitude Test On Individual Wages »
Model 3 Man leaves & joins Shortcuts »
Click to Read...Model 3 Man leaves & joins Online Quiz
Click to Start..time & work Shortcuts and Techniques with Examples
-
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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