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) 13 days
(b) 12 days
(c) 20 days
(d) 15 days
The correct answers to the above question in:
Answer: (b)
Using basics of Rule 2,
Time taken by A to finish the work
= 5 × 6 = 30 days
Time taken by B to complete the work
= ${8 × 5}/2$ = 20 days
(A + B)'s 1 day’s work
= $1/30 + 1/20 = {2 + 3}/60 = 1/12$
Required time = 12 days
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Read more split and fraction of work Based Quantitative Aptitude Questions and Answers
Question : 1
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.
Question : 2
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 : 3
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 : 4
A can do a work in 20 days and B in 40 days. If they work on it together for 5 days, then the fraction of the work that is left is :
a) $8/15$
b) $5/8$
c) $1/10$
d) $7/15$
Answer »Answer: (b)
Using Rule 2,
(A + B)’s 5 days’ work = $5(1/20 + 1/40)$
= $5({2 + 1}/40) = 15/40 = 3/8$
Remaining work = $1 - 3/8 = 5/8$
Question : 5
A does half as much work as B in one-third of the time taken by B. If together they take 10 days to complete a work, then the time taken by B alone to do it would have been
a) 25 days
b) 30 days
c) 12 days
d) 6 days
Answer »Answer: (a)
Using Rule 2,
If B completes a work in x days,
A will complete the same in ${2x}/3$ days.
$1/x + 3/{2x} = 1/10$
${2 + 3}/{2x} = 1/10$
2x = 50 ⇒ x = 25 days
Question : 6
x does $1/4$ of a job in 6 days. y completes rest of the job in 12 days. Then x and y could complete the job together in
a) 9$3/5$ days
b) 9 days
c) 7$1/3$ days
d) 8$1/8$ days
Answer »Answer: (a)
Using Rule 2,
x does $1/4$ work in 6 days
x does 1 work in 24 days
Similarly,
y does $3/4$ work in12 days
y does 1 work in ${12 × 4}/3$ = 16 days
(x + y)’s 1 day’s work
= $1/24 + 1/16 = {2 + 3}/48 = 5/48$
Required time = $48/5 = 9{3}/5$ 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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