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) $28/3$ days
(b) $49/4$ days
(c) $49/3$ days
(d) 11 days
The correct answers to the above question in:
Answer: (d)
Ratio of efficiency of Babu and Asha
= 1 : $7/4$ = 4 : 7.
As the time taken is inversely proportional to efficiency, therefore, if Babu takes 7x days to complete work, Asha will take 4x days.
$1/{7x} + 1/{4x} = 1/7 ⇒ {4 + 7}/{28x} = 1/7$
28x = 11 × 7
$x = {11 × 7}/28 = 11/4$
Asha will complete the work in
$4x = 4 × 11/4$ = 11 days.
Using Rule 22,
Here, n = $7/4$, D = 7
Time taken by Asha= $({n + 1}/n)$D days
= $({{7/4} + 1}/{7/4}) × 7 = 11/7 × 7$ = 11 days
Shortcut : 2
Posted by : Shweta Mahapatra
Posted Date: 2021-07-07 14:17:48
The efficiencies (rate) ratios of Babu and Asha is $1:7/4$
which corresponds to 4:7 and the total rate of Babu and Asha will be 11.
So, the days taken together is given 7 and now by proportionality,
we can calculate 7x=77 and x will be 11 days.
(rate is inversely proportional to days)
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Read more efficiency of the worker Based Quantitative Aptitude Questions and Answers
Question : 1
Sunil completes a work in 4 days, whereas Dinesh completes the work in 6 days. Ramesh works 1$1/2$ times as fast as Sunil. The three together can complete the work in
a) 1$5/19$ days
b) 1$5/12$ days
c) 1$5/7$ days
d) 1$3/8$ days
Answer »Answer: (a)
Using Rule 3If A can do a work in 'x' days, B can do the same work in 'y' days, C can do the same work in 'z' days then, total time taken by A, B and C to complete the work together = $1/{1/x + 1/y + 1/z} = {xyz}/{xy + yz + zx}$and If workers are more than 3 then total time taken by A, B, C ...... so on to complete the work together = $1/{1/x + 1/y + 1/z + ...}$
Time taken by Ramesh
= $4 × 2/3 = 8/3$ days
Work done by all three in 1 day
= $1/4 + 1/6 + 3/8 = {6 + 4 + 9}/24 = 19/24$
Required time
= $24/19 = 1{5}/19$ days
Question : 2
A can do a piece of work in 6 days. B is 25% more efficient than A. How long would B alone take to finish this work?
a) 2$2/3$ days
b) 4$4/5$ days
c) 3$1/3$ days
d) 5$1/4$ days
Answer »Answer: (b)
Ratio of A's and B's efficiency = 4 : 5
Ratio of time taken = 5 : 4
Time taken by B = ${6 × 4}/5$
= $24/5 = 4{4}/5$ days
Using Rule 17,
Here, x = 6, R = 25%
Time taken by B = $x × 100/{100 + R}$ days
= $6 × 100/125 = 6 × 4/5$
= $24/5 = 4{4}/5$ days
Question : 3
A works twice as fast as B. If B can complete a piece of work independently in 12 days, then what will be the number of days taken by A and B together to finish the work?
a) 18
b) 4
c) 6
d) 8
Answer »Answer: (b)
A is twice efficient than B.
Time taken by B = 12 days
Time taken by A = 6 days
(A + B)’s 1 day’s work
= $1/6 + 1/12 = {2 + 1}/12 = 1/4$
∴ Required time = 4 days
Question : 4
A is thrice as good a workman as B and is, therefore, able to finish a piece of work in 60 days less than B. The time (in days) in which they can do it working together is
a) 23$1/4$ days
b) 22 days
c) 22$1/2$ days
d) 23 days
Answer »Answer: (c)
Using Rule 2,
If A completes the work in x days,
B will do the same in 3x days.
3x - x = 60
2x = 60
x = 30 and 3x = 90
(A + B)’s 1 day’s work
= $1/30 + 1/90 = {3 + 1}/90$
= $4/90 = 2/45$
A and B together will do the work in $45/2$ or 22$1/2$ days.
Question : 5
Kamal can do a work in 15 days. Bimal is 50 per cent more efficient than Kamal in doing the work. In how many days will Bimal do that work?
a) 10$1/2$ days
b) 14 days
c) 12 days
d) 10 days
Answer »Answer: (d)
Using Rule 15The comparison of rate of work done is called efficiency of doing work. Efficiency (E) ∝ $1/\text"No. of days"$ E1 : E2 : E3 = $1/D_1 : 1/D_2 : 1/D_3$, E =$k/D$ or, ED =k or, $E_1D_1= E_2D_2$
Efficiency and time taken are inversely proportional Bimal : Kamal = 150 : 100 (work)
100 : 150 (Time) = 2 : 3
Since, 3 units ⇒ 15 days
2 units ⇒ $15/3 × 2$ = 10
Hence, Bimal complete the work in 10 days
Question : 6
A can do a piece of work in 70 days and B is 40% more efficient than A. The number of days taken by B to do the same work is
a) 45 days
b) 40 days
c) 60 days
d) 50 days
Answer »Answer: (d)
A : B = $D_2 : D_1$
100 : 140 = $D_2$ : 70
100 × 70 = 140 × $D_2$
$D_2 = {100 × 70}/140 = 50$ 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 = 70, r = 40%
Time taken by B = $x × 100/{100 + R}$
= ${70 × 100}/{100 + 40}$ = 50 days
time & work Shortcuts and Techniques with Examples
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Model 1 Basics on Time & Work
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Model 2 Formula method ‘M1D1W1 = M2D2W2’
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Model 3 Man leaves & joins
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Model 4 Working with Man, Woman, Child
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Model 5 Split & Fraction of work
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Model 6 Efficiency of the worker
Defination & Shortcuts … -
Model 7 Working with individual wages
Defination & Shortcuts …
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