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) 22.5 days
(b) 25 days
(c) 21 days
(d) 21.4 days
The correct answers to the above question in:
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
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Read more efficiency of the worker Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
5 men and 2 women working together can do four times as much work per hour as a man and a woman together. The work done by a man and a woman should be in the ratio :
a) 4 : 1
b) 1 : 2
c) 2 : 1
d) 1 : 3
Answer »Answer: (c)
5m + 2w = 4m + 4w ⇒ m = 2w
Required ratio = 2 : 1
Question : 3
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 : 4
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 ).
Question : 5
A can do a certain work in 12 days. B is 60% more efficient than A. How many days will B and A together take to do the same job?
a) $60/13$ days
b) $80/13$ days
c) $70/13$ days
d) $75/13$ days
Answer »Answer: (a)
Time taken by B in completing the work
=$12 × 100/160 = 15/2$ days
(A+B)’s 1 day’s work
= $1/12 + 2/15 = {5 + 8}/60 = 13/60$
Hence, the work will be completed in $60/13$ days
Using Rule 17,
Here, x = 12, R = 60%
Time taken by B= $x × 100/{100 + R}$ days
= $12 × 100/160$ days = $15/2$ days
Now using Rule 2,
Time taken by A and B = ${xy}/{x + y}$
= ${12 × {15/2}}/{12 + {15/2}}$
= ${12 × 15}/39 = 60/13$ days
Question : 6
A can do a certain job in 12 days. B is 60% more efficient than A. To do the same job B alone would take :
a) 7 days
b) 7$1/2$ days
c) 8 days
d) 10 days
Answer »Answer: (b)
Time taken by B
= $12 × 100/160 = 15/2 = 7{1}/2$ days
Using Rule 17,
Here, x = 12, R = 60%
Time taken by B = $x × 100/{100 + R}$ days
= $12 × 100/160$ days
= $15/2$ days = 7$1/2$ 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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