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) $2/3$
(b) $1/3$
(c) $1/2$
(d) $1/4$
The correct answers to the above question in:
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 = $4/6 = 2/3$
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Read more split and fraction of work Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
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 : 3
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 : 4
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 : 5
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
Question : 6
Two workers A and B are engaged to do a piece of work. A working alone would take 8 hours more to complete the work than when work together. If B worked alone, would take 4$1/2$ hours more than when work together. The time required to finish the work together is
a) 4 hours
b) 5 hours
c) 6 hours
d) 8 hours
Answer »Answer: (c)
Time taken by A and B = x hours (let).
According to the question,
Time taken by A alone
= (x + 8) hours.
Time taken by B alone
= $(x + 9/2)$ hours.
$1/{x + 8} + 1/{x + {9/2}} = 1/x$
$1/{x + 8} + 2/{2x + 9} =1/x$
${2x + 9 + 2x + 16}/{(x + 8)(2x + 9)} = 1/x$
${4x + 25}/{2x^2 + 16x + 9x + 72} = 1/x$
$4x^2 + 25x = 2x^2 + 25x + 72$
$2x^2 = 72 ⇒ x^2 = 72/2 = 36$
x = $√{36}$ = 6 hours
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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