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The following question based on time & work topic of quantitative aptitude
(a) 37 days
(b) $37{1}/2$ days
(c) 23 days
(d) 40 days
The correct answers to the above question in:
Answer: (b)
Using Rule 2,
A can do the whole work in ${20 × 5}/4 = 25$ days
Remaining work = $1 - 4/5 = 1/5$
(A + B)’s 1 day’s work = $1/15$
and A’s 1 day’s work = $1/25$
B’s 1 day’s work
= $1/15 - 1/25 = {5 - 3}/75 = 2/75$
B can finish the work in $75/2$ days
i.e., 37$1/2$ days
Discuss Form
Read more split and fraction of work Based Quantitative Aptitude Questions and Answers
Question : 1
A can do $1/2$ of a piece of work in 5 days, B can do $3/5$ of the same work in 9 days and C can do $2/3$ of that work in 8 days. In how many days can three of them together do the work ?
a) 5 days
b) 3 days
c) 4 days
d) 4$1/2$ days
Answer »Answer: (c)
Using Rule 3If A can do a work in 'x' days, B can do the same work in 'y' days, C can do the same work in 'z' days then, total time taken by A, B and C to complete the work together = $1/{1/x + 1/y + 1/z} = {xyz}/{xy + yz + zx}$and If workers are more than 3 then total time taken by A, B, C ...... so on to complete the work together = $1/{1/x + 1/y + 1/z + ...}$
A can do $1/2$ work in 5 days.
A can do 1 work in 10 days
Similarly,
B can do 1 work in $5/3$ × 9 = 15 days.
C can do 1 work in 8 × $3/2$ = 12 days.
Now, A’s 1 day’s work = $1/10$
B’s 1 day’s work = $1/15$
C’s 1 day’s work = $1/12$
(A + B + C)’s 1 day’s work = $1/10 + 1/15 + 1/12$
= ${6 + 4 + 5}/60 = 15/60 = 1/4$
Hence, (A + B + C) together can complete the work in 4 days.
Question : 2
4 men and 6 women complete a work in 8 days. 2 men and 9 women also complete in 8 days in which. The number of days in which 18 women complete the work is :
a) 5$1/3$ days
b) 4$1/3$ days
c) 5$2/3$ days
d) 4$2/3$ days
Answer »Answer: (a)
According to the question,
(4 × 8) men + (6 × 8) women ≡
(2 × 8) men + (9 × 8) women
4 men + 6 women ≡ 2 men + 9 women
(4 - 2) men ≡ (9 - 6) women
2 men ≡ 3 women
4 men + 6 women ≡ 12 women
$M_1D_1 = M_2D_2$
12 × 8 = 18 × $D_2$
$D_2 = {12 × 8}/18 = 16/3 = 5{1}/3$ days
Using Rule 11,
Here, $A_1$ = 4, $B_1$ = 6, $D_1$ = 8
$A_2$ = 2, $B_2$ = 9, $D_2$ = 8
$A_3$ = 0, $B_3$ = 18
Required time = ${D_1D_2(A_1B_2 - A_2B_1)}/{D_1(A_1B_3 - A_3B_1) - D_2(A_2B_3 - A_3 B_2)}$ days
= ${8 × 8(4 × 9 - 2 × 6)}/{8(4 × 18 - 0 × 6) - 8(2 × 18 - 0 × 9)}$
= ${64 × 24}/{8 × 72 - 36 × 8} = 192/36$
= $16/3 = 5{1}/3$ days
Question : 3
A can do in one day three times the work done by B in one day. They together finish $2/5$ of the work in 9 days. The number of days by which B can do the work alone is :
a) 120 days
b) 90 days
c) 30 days
d) 100 days
Answer »Answer: (b)
Let time taken by A alone in doing work be x days.
Time taken by B alone = 3x days
A and B together finish $2/5$ work in 9 days.
TIme taken by A and B in doing whole work
= ${9 × 5}/2 = 45/2$ days
$1/x + 1/{3x} = 2/45$
${3 + 1}/{3x} = 2/45$
$4/{3x} = 2/45$ ⇒ 2 × 3x = 4 × 45
$x = {4 × 45}/{2 × 3}$ = 30 days
Time taken by B = 3x days = 3 × 30 = 90 days
Using Rule 22The efficiency of A to work is 'n' times more than that of B, Both start to work together and finish it in 'D' days. Then, A and B will separately complete, the work in $({n + 1}/n)$D and (n + 1)D days respectively.
Here, n = 3 and D = ${9 × 5}/2 = 45/2$ days
(Time taken to finish whole work)
Time taken by B = (n + 1)D
= (3 + 1) × $45/2$ = 90 days
Question : 4
P can do $(1/4)$th of work in 10 days, Q can do 40% of work in 40 days and R can do $(1/3)$rd of work in 13 days. Who will complete the work first?
a) Q
b) P
c) Both P and R
d) R
Answer »Answer: (d)
Since, P does $1/4$ th work in 10 days.
P will do 1 work in 10 × 4 = 40 days
Since, Q, does 40% part of work in 40 days
Q will do 100% work in
${40 × 100}/40$ = 100 days
Since, R, does $1/3$ rd work in 13 days.
R will do 1 work in 13 × 3 = 39 days
Question : 5
A can cultivate $2/5$th of a land in 6 days and B can cultivate $1/3$ rd of the same land in 10 days. Working together A and B can cultivate $4/5$th of the land in:
a) 5 days
b) 4 days
c) 10 days
d) 8 days
Answer »Answer: (d)
Using Rule 2,
The part of field cultivated by A in 1 day
= $2/{5 × 6} = 1/15$
The part of field cultivated by B in 1 day
= $1/{3 × 10} = 1/30$
The part of field cultivated by A and B together
= $1/15 + 1/30 = 3/30 = 1/10$
$4/5$ part of field cultivated by A and B together in
= ${4/5}/{1/10}$ days = ${4 × 10}/5 = 8$ days
Question : 6
A and B work together to complete the rest of a job in 7 days. However, $37/100$ of the job was already done. Also, the work done by A in 5 days is equal to the work done by B in 4 days. How many days would be required by the fastest worker to complete the entire work?
a) 25
b) 20
c) 10
d) 30
Answer »Answer: (b)
Remaining work
= $1 - 37/100 = {100 - 37}/100 = 63/100$
Time taken by (A + B) in doing
$63/100$ part of work = 7 days
Time taken by them in doing whole work
= $100/63 × 7 = 100/9$ days
Respective ratio of time taken by
A and B in doing the work = 5 : 4
$1/{4x} + 1/{5x} = 9/100$
${5 + 4}/{20x} = 9/100$
20x = 100 ⇒ x = 5
Required time = 4 × 5 = 20 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’
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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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