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) 6
(b) 5
(c) 3
(d) 4
The correct answers to the above question in:
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
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Read more split and fraction of work Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
A can do $7/8$ of work in 28 days, B can do $5/6$ of the same work in 20 days. The number of days they will take to complete if they do it together is
a) 17$3/5$ days
b) 15$3/7$ days
c) 13$5/7$ days
d) 14$5/7$ days
Answer »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
Question : 3
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 : 4
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
Question : 5
A can complete a work in 6 days while B can complete the same work in 12 days. If they work together and complete it, the portion of the work done by A is
a) $2/3$
b) $1/3$
c) $1/2$
d) $1/4$
Answer »Answer: (a)
Using Rule 2,
Time taken by A and B
= ${6 × 12}/{6 + 12} = {6 × 12}/18 = 4$
Work done by A in 4 days = $4/6 = 2/3$
Question : 6
A company employed 200 workers to complete a certain work in 150 days. If only one fourth of the work has been done in 50 days, then in order to complete the whole work in time, the number of additional workers to be employed was
a) 300
b) 100
c) 200
d) 600
Answer »Answer: (b)
Using Rule 1,
200 workers do $1/4$ work in 50 days.
How many workers will do $3/4$ work in 100 days ?
Number of additional workers = x (let)
${M_1D_1}/W_1 = {M_2D_2}/W_2$
${200 × 50}/{1/4} = {(200 + x) × 100}/{3/4}$
(200 + x) 100 = 3 × 200 × 50
200 + x = 300
x = 300 - 200 = 100
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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