Latest TCS Aptitude Question SOLUTION: if 20 men or 24 women or 40 boys can do a job in 12days working for 8 hours a day.how many men working with 6 women and 2 boys take to do a job four times as big working 5 hours a

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if 20 men or 24 women or 40 boys can do a job in 12days working for 8 hours a day.how many men working with 6 women and 2 boys take to do a job four times as big working 5 hours a day for 12days?

Asked In TCS ratna (11 years ago)

Unsolved Read Solution (16)

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Read Solution (16) :

neha   (11 years ago)

Amount of work done by 20 men = 24 women = 40 boys or amount of work done by 1 man = 1.2 women = 2 boys.

Let us therefore, find out the amount of men required, if only men were working on the task, to complete the new job under the new conditions.

And then make adjustments for the women and boys who are already employed on the task.

The man hours required to complete the new task = 4 times the man hours required to complete the old task. (As the new task is 4 times as big as the old task)

So, the new task is 20 * 12 * 8 * 4 men hours task.

Let 'n' be the number of men required to complete the new task.
Equating the men hours of task, we get 20 * 12 * 8 * 4 = n * 5 * 12. Or n = 128.

The new task will require 128 men, if only men worked on the task to complete it.

However, the problem states that 6 women and 2 boys are working on the job.

6 women are the equivalent of = 5 men and 2 boys = 1 man.

i.e., the equivalent of 5 + 1 = 6 men are already working on the project.

Therefore, 122 more men are required to work with 6 women and 2 boys to complete the task.

Is this solution Helpfull? Yes (22) | No (6)  

neha   (11 years ago)

my answer is 122

Is this solution Helpfull? Yes (6) | No (5)  

sravani  (9 years ago)

20m=24w=40b
w=5/6 m
b=1/2 m
6w+2b=5m+m=6m
20*8 =x*5
x=32
no of men =32-6=26m

Is this solution Helpfull? Yes (4) | No (1)  

diptangshu paul  (11 years ago)

my last ans was wrong
answer is 122 men...
24w-96hrs-xw
1-8hrs-[x/24]
1w-1hr-[x/24*96]
6w-60hr-[x*6*60/24*96] = 5x/32 work

40b-96hr-x
2b-60 hr - [x*2*60/40*96]= x/32

so total work done by 6w and 2 b = 6x/32
men do [4x-6x/32]= 122x/32

96 hrs- x work - 20 men
1 hrs - x work - 20*96 men
1 hrs- 1 w - [(20*96)/x] men
60 hrs - 122x/32 work -- [(20*96*122x)/(x*60*32)] = 122
so answer is 122 men

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

Ashish Sarkar  (9 years ago)

using m*d*w rule we get
(20*12*8)*4=x*5*12
=>x=128
now 6 women=5 men and 2 boys=1 man;
so already we have 5m+1m=6m then 128-6=122
so 122 men are required .

Is this solution Helpfull? Yes (2) | No   

Rahul singh  (11 years ago)

x=126 men

sol=
m*w*d=m*w*d rule will apply here;
(20+24+40)*12*8=(x+6+2)*12*5;
x=126;
ans

Is this solution Helpfull? Yes (1) | No (6)  

niki  (11 years ago)

@neha: plz explain..

Is this solution Helpfull? Yes (1) | No (1)  

vijaya  (8 years ago)

ans-26
24women............96hours...............1work
6women...............60hours.............6*60/96*24=5/32

40boys...............96hours................1work
2boys..................60hours...............2*60/40*96=1/32

remaining work=1-[5/32+1/32]
1-6//32=13/16

20men.........1hours.........1/96work
1men............1hours.........1/96*20work

1/96*20work.............1hours..........1men
1work...............60hours...........96*20/60=32
13/16work.............60hours............32*13/16=26men.

Is this solution Helpfull? Yes (1) | No   

vishal kumar  (7 years ago)

use the formula
(M1*D1*E1)/V1 = (M2*D2*E2)/V2
where M=no of men
D=duration of work
E=efficency of the work
V=volume of the work
A/Q:
M1=20, M2=X
D1=12*8 ,D2=12*5
E1:E2=4:1
V1=V2=1(SAME JOB)

(20*12*8*4) = X*12*5*1
X=122(MEN)

Is this solution Helpfull? Yes (1) | No (1)  

anindo  (7 years ago)

use m * d * w formula
(20 * 12 * 8) * 4 = x * 12 * 5 [ multiply with 4 because job is done 4 times ]
after solving this we will get x =128men [ total number of men working ]
now, look it is given 20men or 24 women or 40 boys that mens 20men=24 women = 40boys
ab hmlog 1men nikalenge kikitna barabar h woh women aur boys ke...
20men=24women
=> m= 24/20
=>m = 1.2 women
now in case of boys 1 men is equal to 20m=40b
=> m=40/20
=> m= 2 boy ohk
now it is given that 6women and 2 boys lready working now we will use 1men is equal to how much women and boy which we have founf earlier
look, 24women=20men [from 1st part of question]
1 women = 20/24 men
6women=20/24*6 men => 5 men [ 6 women = 5 men].......(1)
and we already know that [2 boy is equal to 1 men]....(2)
now, 6women + 2 boys = 5 men + 1 men = 6 men (using 1 and 2 )
now simply deduct 128 - 6 = 122 [ total men - men already working i.e 6 ]
so 122 answer

Is this solution Helpfull? Yes (1) | No   

ANUSHA   (11 years ago)

i think 126 men required

Is this solution Helpfull? Yes | No (5)  

diptangshu paul  (11 years ago)

answer is 26 men...
24w-96hrs-xw
1-8hrs-[x/24]
1w-1hr-[x/24*96]
6w-60hr-[x*6*60/24*96] = 5x/32 work

40b-96hr-x
2b-60 hr - [x*2*60/40*96]= x/32

so total work done by 6w and 2 b = 6x/32
men do [x-6x/32]= 26x/32

96 hrs- x work - 20 men
1 hrs - x work - 20*96 men
1 hrs- 1 w - [(20*96)/x] men
60 hrs - 26x/32 work -- [(20*96*26x)/(x*60*32)] = 26
so answer is 26 men

Is this solution Helpfull? Yes | No (6)  

snehil  (11 years ago)

(20+24+40):12*8:1=(x+6+2):12*5:4*1
accordind to ques job is 4 times than pre
(20+24+40)*1/12*8 = (x+6+2)*4/(12*5)
solv n find the x

Is this solution Helpfull? Yes | No (1)  

Rahul Sachan  (11 years ago)

answer is 122-6=116

Is this solution Helpfull? Yes | No (1)  

harshita verma  (8 years ago)

Let’s try solving this Problem using ratio approach.
Amount of work done by 20 men = 24 women = 40 boys or 1 man = 1.2 woman = 2 boys.

Let us therefore, find out the amount of men required, if only men were working on the job, to complete the new job under the new conditions and then make adjustments for the women and children working with the men.

The man hours required to complete the new job = 4 times the man hours required to complete the old job. (As the new job is 4 times as big as the old job)
Let ‘n’ be the number of men required.

20×12×8=n×5×12×4 or n=8

8 men working will be able to complete the given job.

However, the problem states that 6 women and 2 boys are working on the job.

6 women = 612= 5 men and 2 boys = 1 man. The equivalent of 5+1=6 men are already working.
.

Is this solution Helpfull? Yes | No   

neelabh rai  (8 years ago)

let us take number of men = x
now ,
24 w = 20 m
1 w = 20/24 m
and
40 b = 20 m
so , 1 b = 20/40 m

now ,according to the second conditon
total number if people in terms of men =
x +(20/24)*6+(20/40)*2 = x+ 5+1 = (6+x) men
now a.t.q
(m1)(d1)(t1)=(m2)(d2)(t2)
20*12*8= (6+x)*5*12
20*8=(6+x)*5
32=6+x
X=26

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