Model 6 Efficiency of the worker 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) 18 days
(b) 10 days
(c) 12 days
(d) 15 days
The correct answers to the above question in:
Answer: (d)
Time taken by B
= ${21 × 100}/140$ = 15 days
Using Rule 17If A can do a work in 'x' days and B is R% more efficient than A, then 'B' alone will do the same work in $x × 100/{100 + R}$ days
Here, x = 21, R = 40%
Time taken By B = $x × 100/{100 + R}$ days
= $21 × 100/140$ days = 15 days
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Read more efficiency of the worker Based Quantitative Aptitude Questions and Answers
Question : 1
A takes twice as much time as B and thrice as much as C to complete a piece of work. They together complete the work in1 day. In what time, will A alone complete the work.
a) 4 days
b) 9 days
c) 5 days
d) 6 days
Answer »Answer: (d)
Let time taken by C to complete the work = x days
Time taken by A to complete the work = 3x days
and time taken by B to complete the work = ${3x}/2$ days
According to the question,
$1/{3x} + 1/{{3x}/2} + 1/x = 1$
$1/{3x} + 2/{3x} + 1/x = 1$
${1 + 2 + 3}/{3x} = 1$
$6/{3x} = 1 ⇒ 2/x = 1 ⇒ x = 2$
Time taken by A
= 3x = 3 × 2 = 6 days
Question : 2
If 10 people can do a job in 20 days, then 20 people with twice the efficiency can do the same job in
a) 40 days
b) 5 days
c) 10 days
d) 20 days
Answer »Answer: (b)
In second case, the efficiency of a man is twice to that in the first case.
$M_1D_1 = M_2D_2$
10 × 20 = 2 × 20 × $D_2$
$D_2 = {10 × 20}/{2 × 20}$ = 5 days.
Question : 3
P is thrice as good a workman as Q and therefore able to finish a job in 48 days less than Q. Working together, they can do it in :
a) 12 days
b) 18 days
c) 24 days
d) 30 days
Answer »Answer: (b)
Using Rule 2,
Let time taken by P = x days
Then, time taken by Q = 3x days
3x - x = 48 ⇒ x = 24
(P + Q)’s 1 day’s work
= $1/24 + 1/72 = {3 + 1}/72 = 1/18$
Required time = 18 days
Question : 4
A takes 10 days less than the time taken by B to finish a piece of work. If both A and B can do it in 12 days, then the time taken by B alone to finish the work is
a) 25 days
b) 30 days
c) 27 days
d) 20 days
Answer »Answer: (b)
Using Rule 2,
Let time taken by B in completing the work = x days
Time taken by A = (x - 10) days
⇒ $1/x + 1/{x - 10} = 1/12$
⇒ ${x - 10 + x}/{x(x - 10)} = 1/12$
⇒ $24x - 120 = x^2 - 10x$
⇒ $x^2 - 34x + 120$ = 0
⇒ $x^2 - 30x - 4x + 120$ = 0
⇒ $x (x - 30) - 4 (x - 30)$ = 0
⇒ $(x - 4) (x - 30)$ = 0
⇒ $x = 30$ because $x ≠ 4$
Question : 5
A is 50% as efficient as B. C does half of the work done by A and B together. If C alone does the work in 20 days, then A, B and C together can do the work in
a) 7 days
b) 5$2/3$ days
c) 6$2/3$ days
d) 6 days
Answer »Answer: (c)
If B alone completes the work in x days, A will do the same in 2x days.
(A + B)’s 1 day’s work = $1/x + 1/{2x} = {2 + 1}/{2x} = 3/{2x}$
and C’s 1 day’s work = $3/{4x}$
$3/{4x} = 1/20$
4x = 3 × 20
$x = {3 × 20}/4 = 15$
(A + B + C)’s 1day’s work
= $1/{2x} + 1/x + 3/{4x} = 1/30 + 1/15 + 1/20$
= ${2 + 4 + 3}/60 = 9/60 = 3/20$
Hence, all three together will complete the work in
$20/3$ or $6{2}/3$ 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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