GATE CSE 2010 | Question: 64

Question

$5$ skilled workers can build a wall in $20$ days; $8$ semi-skilled workers can build a wall in $25$ days; $10$ unskilled workers can build a wall in $30$ days. If a team has $2$ skilled, $6$ semi-skilled and $5$ unskilled workers, how long it will take to build the wall?

• A. $20$ days
• B. $18$ days
• C. $16$ days
• D. $15$ days

Comments

Take work as lcm of days lcm(20,25,30) which is equal to 300 so total 300 unit of work 

5 skill worker can build a wall in 20 days so amount of work done in 1 day=300/20=>15 unit

1 skill worker will do less amount of work in 1 day so 15/5=3 unit 

8 semi skill worker build a wall in 25 days so amount of unit of work done in 1 day by them=300/25=12 unit of work

1 semi skill worker will do 12/8 unit of work in 1 day

10 unskilled worker build a wall in 30 days so amount of unit of work done in 1 day=300/30=10 unit of work

1 unskilled worker will do 10/10=1 unit of work

amount of unit of work done by 2 skilled 6 semi-skilled 5 unskilled worker in 1 day

2*3+6*12/8+5*1=6+9+5=20 unit of work in 1 day

total unit of work =300 so

300/20=15 days.

option D

 

 

Answer 1

D. $15$ days

$1$ skilled person can do $\frac{1}{20 \times 5} = 1/100$ of work in $1$ day, so $2$ skilled person do $2/100$ of work in a day.

Similarly, $6$ semi-skilled and $5$ unskilled person can do $6/200$ and $5/300$ of work respectively in $1$ day.

So, together they do $\frac{2}{100}+\frac{6}{200}+\frac{5}{300} = \frac{1}{15}$ of work together in $1$ day, which gives required number of day to complete the work $= 15.$

Comments

5 / 300 instead of 5300

btw amazing solution

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you gave the best practice to solve this type of questions, Thank You

Answer 2

$5\times 20\ SW-D=8\times 25\ SSW-D=10\times 30\ USW-D\ \ \ .............(1)$

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$5\times 20\ SW-D=10\times 30\ USW-D$

$1\ SW=3\ USW$

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$8\times 25\ SSW-D=10\times 30\ USW-D$

$2\ SSW=3\ USW$

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If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers

$2\ SW+ 6\ SSW+ 5\ USW$

$6\ USW+6\times \dfrac{3\ USW}{2}+5\ USW=20\ USW$

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$10\ USW\rightarrow 30\ days$

$20\ USW\rightarrow ?$

$?=15\ days$

Answer 3

D: 15 days

5 skilled:- 20 days, so 1 skilled done in 20*5 days = 100 days 

2 skilled done in 100/2= 50 days.   , similarly, 6 semi-skilled done in 200/6

similarly, 5 unskilled done  in 300/5 = 60

M: Manpower, R: Rate, T : Time, W: Work done

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M        2 skilled (s)                     6 semi-skilled (ss)           5 unskilled (us)              s+ ss+ us

R        12                                            18                                        10                            40

T        50  days                            200/6 days                       60 days                             x

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W       600                                 600                                   600                                  600

 

take LCM(50,100/3,30) = [ LCM(50,200,30) / HCF(1,6,1) ] = 600/1= 600

Rate = W/T

Rate of s+ss+us = 12+18+10= 40

 

x=600/40 = 15 days