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) 25
(b) 15
(c) 16
(d) 18
The correct answers to the above question in:
Answer: (c)
Time taken by Shashi in doing 1 work = 20 days
Tanya is 25% more efficient than Shashi.
Time taken by Tanya
= $100/125 × 20$ = 16 days
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Read more efficiency of the worker Based Quantitative Aptitude Questions and Answers
Question : 1
A is 30% more efficient than B, and can alone do a work in 23 days. The number of days, in which A and B, working together can finish the job is
a) 21 days
b) 11 days
c) 13 days
d) 20 days
Answer »Answer: (c)
Using Rule 2,
Time taken by B
= $130/100 × 23 = 299/10$ days
(A + B)’s 1 day’s work
= $1/23 + 10/299$
= ${13 + 10}/299 = 23/299 = 1/13$
Time taken by (A + B) = 13 days
Question : 2
To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it ?
a) 45 days
b) 30 days
c) 35 days
d) 40 days
Answer »Answer: (b)
Using Rule 2If A completes a piece of work in 'x' days, and B completes the same work in 'y' days, then,Work done by A in 1 day = $1/x$, Work done by B in 1 day = $1/y$ Work done by A and B in 1 day = $1/x + 1/y = {x + y}/{xy}$Total time taken to complete the work by A and B both = $({xy}/{x + y})$
Let B alone can do the work in x days.
A can do the work in ${3x}/2$ days.
According to the question,
$1/x + 2/{3x} = 1/18 ⇒ {3 + 2}/{3x} = 1/18$
$5/{3x} = 1/18 ⇒ 3x = 18 × 5$
$x = {18 × 5}/3$ = 30 days
Question : 3
A is thrice as good a workman as B and therefore is able to finish a job in 40 days less than B. Working together, they can do it in
a) 15 days
b) 14 days
c) 13 days
d) 20 days
Answer »Answer: (a)
Using Rule 2,
Time taken by A to complete the work = x days
Time taken by B to complete the work = 3x days
So, 3x - x = 2x = 40
x = 20 and 3x = 60
(A + B)’s 1 day’s work
= $1/20 + 1/60 = {3 + 1}/60 = 4/60 = 1/15$
A and B together will complete the work in 15 days.
Question : 4
A can do a work in 5 days less than the time taken by B to do it. If both of them together take11$1/9$ days, then the time taken by ‘B’ alone to do the same work (in days) is
a) 30
b) 15
c) 20
d) 25
Answer »Answer: (d)
Using Rule 2,
If the time taken by B to complete the work be x days,
then time taken by A = (x - 5) days
$1/x + 1/{x - 5} = 9/100$
⇒ ${x - 5 + x}/{x(x - 5)} = 9/100$
⇒ $9x^2 - 45x = 200x –500$
⇒ $9x^2 - 245x + 500 = 0$
⇒ $9x^2 - 225x - 20x + 500 = 0$
⇒ $9x (x - 25) - 20 (x - 25)$ = 0
⇒ $(x - 25) (9x - 20)$ = 0
⇒ $x = 25$ because $x ≠ 20/9$
Question : 5
A does 20% less work than B. If A can complete a piece of work in 7$1/2$ hours, then B can do it in
a) 5 hours
b) 6$1/2$ hours
c) 6 hours
d) 5$1/2$ hours
Answer »Answer: (c)
A does 20% less work than B.
Ratio of time taken = 5 : 4
A completes a work in $15/2$ hours
Time taken by B to do the same work
= $15/2 × 4/5$ = 6 hours.
Question : 6
Jyothi can do $3/4$ of a job in 12 days. Mala is twice as efficient as Jyothi. In how many days will Mala finish the job ?
a) 16 days
b) 6 days
c) 8 days
d) 12 days
Answer »Answer: (c)
Using Rule 1If $M_1$ men can finish $W_1$ work in $D_1$ days and $M_2$ men can finish $W_2$ work in $D_2$ days then, Relation is${M_1D_1}/{W_1} = {M_2D_2}/{W_2}$ andIf $M_1$ men finish $W_1$ work in $D_1$ days, working $T_1$ time each day and $M_2$ men finish $W_2$ work in $D_2$ days, working $T_2$ time each day, then${M_1D_1T_1}/{W_1} = {M_2D_2T_2}/{W_2}$
Jyothi can do $3/4$ th of a job in 12 days.
Jyothi can do 1 job in ${12 × 4}/3$ = 16 days.
As Mala is twice as efficient as Jyothi,
Mala will finish the job in 8 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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