Latest TCS Aptitude Question SOLUTION: Mr.P,Mr.Q and Mr.R takes a project and they can complete in 36 hours , 54 hours and 72 hours respectively. Unfortunately Mr.P met an accident and left from the project 8 hours befo

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(#M40033796) TCS Numerical Ability question TIME N WORK Keep an EYE

Mr.P,Mr.Q and Mr.R takes a project and they can complete in 36 hours , 54 hours and 72 hours respectively. Unfortunately Mr.P met an accident and left from the project 8 hours before the completion while Mr.Q left 12 hours before the completion. Then for how many hours did Mr.r worked?

a) 24
b) 18
c) 42
d) 36

Asked In TCS ADIL (10 years ago)

Solved RAHUL PRASAD Read Solution (13)

Is this Puzzle helpful?   (35)   (6) Submit Your Solution Time and Work

Read Solution (13) :

RAHUL PRASAD  (10 years ago)

Assume that the project has to be completed in X hours.
So R has worked for X hours.

Since P has left 8 hours before completion, he worked for X - 8 hours and
Q had left 12 hours before, his participation in work is for X - 12 hours.

Therefore (X - 8) + (X - 12) + X = 1(completion of project)
P can complete a project in 36 hours.
In (X - 8) hours P can complete = (X - 8) / 36

Similarly, Q can complete a project in 54 hours.
In (X - 12) hours P can complete = (X - 12) / 54

In X hours R can complete = X / 72

(X - 8) / 36 + (X - 12) / 54 + X / 72 = 1
6 (X - 8) + 4(X - 12) + 3X = 216
13X = 312
X = 24
Hence the required answer is 24 hours.

Is this solution Helpfull? Yes (69) | No (2)  

shalini  (10 years ago)

(x-8)/36+(x-12)/54+x/72=1
12(x-8)+8(x-12)+6x=432
x=24

Is this solution Helpfull? Yes (11) | No (4)  

siddhant jain  (10 years ago)

let us take lcm of time taken by p,q,r that is 216 work now find per hour work , that is p= 216/36=6 similarly for q=4work per hour and r= 3 work per hour now taking option to satisfy condition takin a that is 24 so for first 12 hour all work togather thats is adding every one per day work
6+4+3= 13 ,13*12 =156 work now after this q left noe p and r work together so 6+3=9 so for next 4 days 9*4=36 noe for rest 8 day only r will work . so 8*3=24 adiing all work 156+36+24=216 so total work = calculated work so this is correct answer .

Is this solution Helpfull? Yes (9) | No   

krishna  (10 years ago)

Assume that the project has to be completed in X hours.
So R has worked for X hours.

Since P has left 8 hours before completion, he worked for X - 8 hours and
Q had left 12 hours before, his participation in work is for X - 12 hours.

Therefore (X - 8) + (X - 12) + X = 1(completion of project)
P can complete a project in 36 hours.
In (X - 8) hours P can complete = (X - 8) / 36

Similarly, Q can complete a project in 54 hours.
In (X - 12) hours P can complete = (X - 12) / 54

In X hours R can complete = X / 72

(X - 8) / 36 + (X - 12) / 54 + X / 72 = 1
6 (X - 8) + 4(X - 12) + 3X = 216
13X = 312
X = 24
Hence the required answer is 24 hours.

Is this solution Helpfull? Yes (2) | No (3)  

subramanian.s  (10 years ago)

Assume that the project has to be completed in X hours.
So R has worked for X hours.

Since P has left 8 hours before completion, he worked for X - 8 hours and
Q had left 12 hours before, his participation in work is for X - 12 hours.

Therefore (X - 8) + (X - 12) + X = 1(completion of project)
P can complete a project in 36 hours.
In (X - 8) hours P can complete = (X - 8) / 36

Similarly, Q can complete a project in 54 hours.
In (X - 12) hours P can complete = (X - 12) / 54

In X hours R can complete = X / 72

(X - 8) / 36 + (X - 12) / 54 + X / 72 = 1
6 (X - 8) + 4(X - 12) + 3X = 216
13X = 312
X = 24
Hence the required answer is 24 hours.

Is this solution Helpfull? Yes (2) | No   

Indranil Ghosh  (9 years ago)

(x-8)/36+(x-12)/54+x/72=1
12(x-8)+8(x-12)+6x=432
x=24

Is this solution Helpfull? Yes (1) | No   

raghav jha  (9 years ago)

Let x be the total hour taken by r to complete the work
p 36 - 6 WORK/HOUR
q 54 LCM (216) -4 WORK/HOUR
r 72 -3 WORK/HOUR

here 216 is the total work

p works for (x-8)hours
q works for (x-12)hours
r works for (x)hours

thus
6*(x-8)+4*(x-12)+3*x=216

after solving this equation
we get x=24

hence ans is 24

Is this solution Helpfull? Yes (1) | No   

abhishek singh  (10 years ago)

42 is the answer....

Is this solution Helpfull? Yes | No (19)  

geetha  (10 years ago)

24 is the ans

Is this solution Helpfull? Yes | No (1)  

chaitra  (10 years ago)

(x-8)/36+(x-12)/54+x/72=1
6(x-8)+4(x-12)+3x=216
6x-48+4x-48+3x=216
13x=312
x=24
ana:a

Is this solution Helpfull? Yes | No   

Supriya_kamkar  (9 years ago)

let xhrs be the time for completion of work
then,p's 1hr work->1/36 & he works for x-8 hrs
q's 1hr work->1/54 & he works for x-12 hrs
r's 1hr work->1/72 & he works for x hrs

(x-8)/36+(x-12)/54+x/72=1

so ans is x= (a) 24

Is this solution Helpfull? Yes | No   

SHUBHAM BHADAURIYA  (9 years ago)

x-8/36 + x-12/54 + x/72 = 1
so x= 24 hrs

Is this solution Helpfull? Yes | No   

raghavendra prasad  (8 years ago)

X(1/36+1/54+1/72)+8(1/54+1/72)+1/12(1/36+1/72)=1
SOLVE FOR X
X=4
SO R WORKED FOR 4+8+12=24 HRS

Is this solution Helpfull? Yes | No   

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