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) 4 : 1
(b) 1 : 2
(c) 2 : 1
(d) 1 : 3
The correct answers to the above question in:
Answer: (c)
5m + 2w = 4m + 4w ⇒ m = 2w
Required ratio = 2 : 1
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Read more efficiency of the worker Based Quantitative Aptitude Questions and Answers
Question : 1
A and B together can do a work in 12 days. B and C together do it in 15 days. If A’s efficiency is twice that of C, then the days required for B alone to finish the work is
a) 15 days
b) 60 days
c) 30 days
d) 20 days
Answer »Answer: (d)
(A + B)’s 1 day’s work = $1/12$ ... (i)
(B + C)’s 1 day’s work = $1/15$ ... (ii)
Difference between A and C’s 1 day’s work
= $1/12 - 1/15 = {5 - 4}/60 = 1/60$
If A alone completes the work in x days, C will do the same in 2x days.
$1/x - 1/{2x} = 1/60$
${2 - 1}/{2x} = 1/60$
$1/{2x} = 1/60 ⇒ x = 30$
B’s 1 day’s work
= $1/12 - 1/30$ [From equation (i)]
= ${5 - 2}/60 = 3/60 = 1/20$
Hence, B alone will complete the work in 20 days.
Question : 2
A is twice as good as B and together they finish a piece of work in 16 days. The number of days taken by A alone to finish the work is
a) 24 days
b) 20 days
c) 21 days
d) 22 days
Answer »Answer: (a)
A is twice as good as B.
Time taken by A = x days
Time taken by B = 2x days
According to the question,
$1/x + 1/{2x} = 1/16$
${2 + 1}/{2x} = 1/16$
$3/x = 1/8$
x = 3 × 8 = 24 days
Question : 3
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
Question : 4
A man does double the work done by a boy in the same time. The number of days that 3 men and 4 boys will take to finish a work which can be done by 10 men in 8 days is
a) 8$4/5$
b) 4
c) 16
d) 7$3/11$
Answer »Answer: (c)
According to the question,
1 man ≡ 2 boys
3 men + 4 boys ≡ (3 + 2) men ≡ 5 men
$M_1D_1 = M_2D_2$
5 × $D_1$ = 10 × 8
$D_1 = {10 × 8}/5$ = 16 days
Question : 5
A and B together can complete a work in 15 days. A is 50% more efficient worker than B. How long will A take to complete the work alone ?
a) 22.5 days
b) 25 days
c) 21 days
d) 21.4 days
Answer »Answer: (b)
Ratio of the work of A and B done in 1 day = 3 : 2
[Since, B's work doen = x (let), then A's work done = ${x + 50}/100 x = 3/2 x$ So, (A : B)'s work done = $3/2 x : x$ or 3 : 2 ]
Since, Work done by A and B together in 1 day = $1/15$
A’s 1 day’s work = $1/15 × 3/5= 1/25$
Hence, A alone will finish the work in 25 days.
Using Rule 22,
Here, n = $3/2$ because A is 50% more efficient than B.
D = 15
Time taken by A = $({n + 1}/n)$D days
= $({{3/2} + 1}/{3/2}) × 15$ = 25 days
Question : 6
A and B can do a job together in 12 days. A is 2 times as efficient as B. In how many days can B alone complete the work ?
a) 12 days
b) 18 days
c) 9 days
d) 36 days
Answer »Answer: (d)
Using Rule 2,
If A alone completes the work in x days, B will complete the same in 2x days.
$1/x + 1/{2x} = 1/12$
${2 + 1}/{2x} = 1/12 ⇒ 2x = 36$
B alone will complete the work in 36 days (i.e. 2x ).
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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