Model 5 Split & Fraction of work 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) $4/3$
(b) $3/4$
(c) $1/4$
(d) $3/20$
The correct answers to the above question in:
Answer: (c)
Using Rule 2
Work done by A and B in 1 day
= $1/10 + 1/20 = {2 + 1}/20 = 3/20$
(A + B)’s 5 days’ work
= ${5 × 3}/20 = 3/4$
Remaining work = $1 - 3/4 = 1/4$
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Read more split and fraction of work Based Quantitative Aptitude Questions and Answers
Question : 1
A does half as much work as B in three fourth of the time. If together they take 18 days to complete the work, how much time will B alone take to do it ?
a) 45 days
b) 40 days
c) 30 days
d) 50 days
Answer »Answer: (c)
Let the time taken by B in doing the work alone = x days
According to the question,
Time taken by A = $2 × {3x}/4 = {3x}/2$ days
$1/x + 1/{{3x}/2} = 1/18$
$1/x + 2/{3x} = 1/18$
${3 + 2}/{3x} = 1/18$
3x = 18 × 5
$x = {18 × 5}/3$ = 30 days
Question : 2
Dhiru can dig $1/a$ of a field in 20 hours. What fraction of the same field can Kaku dig in 20 hours if the two of them can dig the field in 60 hours, working together at their respective rates ?
a) $1/{3a}$
b) ${(a - 3)}/a$
c) ${(a - 3)}/{3a}$
d) ${3a}/{(a - 3)}$
Answer »Answer: (c)
Dhiru digs $1/a$ part of field in 20 hours.
Dhiru digs 1 part of field in 20a hours.
= $1/60 - 1/{20a} = {a - 3}/{60a}$
Part of field dug by Kaku in 1 hour
= ${20(a - 3)}/{60a} ={a - 3}/{3a}$
Question : 3
A can do a certain job in 12 days. B is 60% more efficient than A. Then B can do the same piece of work in
a) 7$1/2$ days
b) 8 days
c) 6 days
d) 6$1/4$ days
Answer »Answer: (a)
A can do a work in 12 days.
B is 60% more efficient than A.
Time taken by B = $(100/160 × 12)$ days
= $15/2 = 7{1}/2$ days
Question : 4
John does $1/2$ piece of work in 3 hours, Joe does $1/4$ of the remaining work in 1 hour and George finishes remaining work in 5 hours. How long would it have taken the three working together to do the work ?
a) 3$1/7$ hours
b) 2$1/7$ hours
c) 2$8/11$ hours
d) 3$8/11$hours
Answer »Answer: (c)
According to the question,
John does $1/2$ work in 3 hours.
Time taken by John in doing whole work = 6 hours
Joe does $1/8$ work in 1 hour.
Time taken by Joe in doing whole work = 8 hours
Remaining work
= $1/2 - 1/8 = {4 - 1}/8 = 3/8$ parts
Time taken by George
= ${8 × 5}/3 = 40/3$ hours
Work done by all three in 1 hour
= $1/6 + 1/8 + 3/40$
= ${20 + 15 + 9}/120 = 44/120 = 11/30$
Required time = $30/11 = 2{8}/11$ hours
Question : 5
A can do one and a half as much of a work which B can do in one day. B alone can do a piece of work in 18 days. They together can finish that work in
a) 11$1/5$ days
b) 10$1/5$ days
c) 7$1/5$ days
d) 5$1/5$ days
Answer »Answer: (c)
Using Rule 2,
Ratio of efficiency of A and B = 3 : 2
Ratio of time taken = 2 : 3
Time taken by A
= $2/3$ × 18 = 12 days
(A + B)’s 1 day’s work
= $1/12 + 1/18 = {3 + 2}/36 = 5/36$
Required time = $36/5 = 7{1}/5$ days
Question : 6
A can complete $1/3$ of a work in 5 days and B, $2/5$ of the work in 10 days. In how many days both A and B together can complete the work ?
a) 9$3/8$ days
b) 10 days
c) 7$1/2$ days
d) 8$4/5$ days
Answer »Answer: (a)
Using Rule 2,
Time taken by A alone in doing the work = 15 days
Time taken by B alone in doing the work
= ${10 × 5}/2$ = 25 days
(A + B)’s 1 day’s work
= $1/15 + 1/25 = {5 + 3}/75 = 8/75$
Hence, the work will be completed in $75/8 = 9{3}/8$ 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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