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) 17$3/5$ days
(b) 15$3/7$ days
(c) 13$5/7$ days
(d) 14$5/7$ days
The correct answers to the above question in:
Answer: (c)
Using Rule 2,
A does $7/8$ work in 28 days.
A will complete the work in
$28 × 8/7$ = 32 days.
B does $5/6$ work in 20 days.
B will complete the work in
${20 × 6}/5$ = 24 days
(A + B)’s 1 day’s work
= $1/32 + 1/24 = {3 + 4}/96 = 7/96$
Required time = $96/7 =13{5}/7$ days
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Read more split and fraction of work Based Quantitative Aptitude Questions and Answers
Question : 1
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
Question : 2
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 : 3
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 : 4
A contractor was engaged to construct a road in 16 days. After working for 12 days with 20 labours it was found that only $5/8$th of the road had been constructed. To complete the work in stipulated time the number of extra labours required is :
a) 10
b) 18
c) 16
d) 12
Answer »Answer: (c)
Using Rule 1,
Remaining work
= $1 - 5/8 = 3/8$ ;
Remaining time = 4 days
${M_1D_1}/W_1= {M_2D_2}/W_2$
${20 × 12}/{5/8} = {M_2 × 4}/{3/8}$
${20 × 12}/5 = {M_2 × 4}/3$
4 × 12 = ${M_2 × 4}/3$
$M_2$ = 12 × 3 = 36
Number of additional workers = 36 - 20 = 16
Question : 5
If 28 men complete $7/8$ of a piece of work in a week, then the number of men, who must be engaged to get the remaining work completed in another week, is
a) 6
b) 5
c) 3
d) 4
Answer »Answer: (d)
Using Rule1,
Work | Days | Men |
$7/8$ | 7 | 28 |
↓ | ↓ | ↓ |
$1/8$ | 7 | x |
$7/8 : 1 8 : : 28 : x$
where x is no. of men
$7/8 × x = 1/8 × 28$
$x = {28 × 8}/{7 × 8}$ = 4
Question : 6
A alone can do a piece of work in 20 days and B alone in 30 days. They begin to work together. They will finish half of the work in :
a) 9 days
b) 8 days
c) 6 days
d) 12 days
Answer »Answer: (c)
(A+B)’s 1 day’s work
= $1/20 + 1/30 = {3 + 2}/60 = 1/12$
Work done in 6 days = $6/12 = 1/2$
Using Rule 2,
Here, x = 20, y = 30
They do the work in = ${xy}/{x + y}$ days
= ${20 × 30}/{20 + 30}$ = 12 days
Half of the work they do in 6 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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