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The following question based on time & work topic of quantitative aptitude
(a) 3
(b) 4
(c) 5
(d) 2
The correct answers to the above question in:
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.
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Read more man leaves and joins Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
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 : 3
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 : 4
X alone can complete a piece of work in 40 days. He worked for 8 days and left. Y alone completed the remaining work in 16 days. How long would X and Y together take to complete the work ?
a) 14 days
b) 15 days
c) 16$2/3$ days
d) 13$1/3$ days
Answer »Answer: (d)
Part of the work done by X in 8 days.
=$8/40 = 1/5$
[Since, work done in 1 day = $1/40$]
Remaining work = $1 - 1/5 = 4/5$
This part of work is done by Y in 16 days.
Time taken by Y in doing 1 work
= ${16 × 5}/4$ = 20 days
Work done by X and Y in 1 day
= $1/40 + 1/20 = {1+2}/40 = 3/40$
Hence, both together will complete the work in $40/3$
i.e.$13{1}/3$ days.
Question : 5
A and B can do a work in 18 and 24 days respectively. They worked together for 8 days and then A left. The remaining work was finished by B in :
a) 5$1/3$ days
b) 8 days
c) 10 days
d) 5 days
Answer »Answer: (a)
Since, A can finish the work in 18 days.
A’s one day’s' work = $1/18$
Similarly, B’s one day’s work = $1/24$
(A + B)’s 8 days’ work = $(1/18 + 1/24) × 8 = 7/72 × 8 = 7/9$
Remaining work = $1 - 7/9 = 2/9$
Time taken to finish the remaining work by B is $2/9 × 24 = 16/3 = 5{1}/3$ 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 = 18, n= 24 and p = 8
Required Time = ${18 × 24 - 8(18 + 24)}/18$
= ${432 - 336}/18 = 96/18$
= $16/3 = 5{1}/3$ days
Question : 6
A can complete a piece of work in 10 days, B in 15 days and C in 20 days. A and C worked together for two days and then A was replaced by B. In how many days, altogether, was the work completed ?
a) 10 days
b) 6 days
c) 8 days
d) 12 days
Answer »Answer: (c)
Work done by (A + C) in 2 days
= $2(1/10 + 1/20) = 2({2 + 1}/20) = 6/20 = 3/10$
Remaining work = $1 - 3/10 = 7/10$
(B + C)’s 1 day’s work
= $1/15 + 1/20 = {4 + 3}/60 = 7/60$
Time taken by (B + C) to finish $7/10$ part of the work
= $60/7 × 7/10$ = 6 days
Total time = 2 + 6 = 8 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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