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) 5 hours
(b) 6$1/2$ hours
(c) 6 hours
(d) 5$1/2$ hours
The correct answers to the above question in:
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.
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Read more efficiency of the worker Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
Shashi can do a piece of work in 20 days. Tanya is 25% more efficient than Shashi. The number of days taken by Tanya to do the same piece of work is :
a) 25
b) 15
c) 16
d) 18
Answer »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
Question : 3
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 : 4
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.
Question : 5
If A, B and C can complete a work in 6 days. If A can work twice faster than B and thrice faster than C, then the number of days C alone can complete the work is :
a) 11 days
b) 33 days
c) 44 days
d) 22 days
Answer »Answer: (b)
Using Rule 3,
Let time taken by A = x days
Time taken by B = 2x days
Time taken by C = 3x days
According to the question,
$1/x + 1/{2x} + 1/{3x}$ = 1 6
${6 + 3 + 2}/{6x} = 1/6$
$11/{6x} = 1/6$
6x = 6 × 11
$x = {6 × 11}/6$ = 11
Time taken by C alone = 3x = 3 × 11 = 33 days
Question : 6
Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked $1/3$ as efficiently as he actually did, the work would have been completed in 3 days. To complete the job alone, A would require
a) 8$3/4$ days
b) 5$1/5$ days
c) 6$1/4$ days
d) 7$1/2$ days
Answer »Answer: (c)
Using Rule 2,
If A alone does the work in x days and B alone does the work in y days, then
$1/x + 1/y = 1/5$ ...(i)
Again, $2/x + 1/{3y} = 1/3$ ...(ii)
By equation (ii) × 3 - (i),
$6/x + 1/y - 1/x - 1/y = 1 - 1/5$
$6/x - 1/x = 4/5$
${6 - 1}/x = 4/5$
$x = 25/4 = 6{1}/4$ 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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