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) 9 days
(b) 8 days
(c) 6 days
(d) 12 days
The correct answers to the above question in:
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
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Read more split and fraction of work Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
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 : 3
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 : 4
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 : 5
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
Question : 6
A does $7/10$ part of work in 15 days. After that he completes the remaining work in 4 days with the help of B. In how many days will A and B together do the same work ?
a) 12$2/3$ days
b) 10$1/3$ days
c) 8$1/4$ days
d) 13$1/3$ days
Answer »Answer: (d)
Using Rule 2,
Remaining work = $1 - 7/10 = 3/10$
(A + B) take 4 days to do $3/10$ work
(A + B) will do the work in $4 × 10/3$ days
= $40/3 =13{1}/3$ 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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