Rohan and Suraj can do a piece of work in 12 days; Suraj and Mahesh in 15 days; Mahesh and Rohan in

M4maths Previous Puzzles

15 Jul 2016 Time and work

Rohan and Suraj can do a piece of work in 12 days; Suraj and Mahesh in 15 days; Mahesh and Rohan in 20 days. In how many days will they finish it together.

OPtion

1) 8
2) 10
3) 12
4) 15
5) 6
6) 9
7) 14
8) 16
9) 18
10)None of these

Solution

(R+S)'s day's work = 1/12;
(S+M)'s 1 day's work = 1/15
(M+R)'s 1 days's work = 1/20

Adding : 2(R+S+M)'s 1 day's work = (1/12 + 1/15 + 1/20)
= 12/60 = 1/5
=> (R+S+M)'s 1 day's work = 1/10
So, they together can finish the work in 10 days.
Option 2)

Correct Option: 2 Best Solution (20)

Razen Yadav   8 years AGO

Rohan and Mohan do work in 1 day =1/12
Similarly Suraj and Mahesh do work in 1 day=1/15
and Mahesh and Rohan do work in 1 day=1/20

adding above 3 eqn
2(Rohan+Suraj+Mahesh)=1/12+1/15+1/20
===(5+4+3)/60
===12/60
===1/5
2(Rohan+Suraj+Mahesh)=1/5
Rohan+Suraj+Mahesh=1/10
means they will do it together in 10 days

Like? Yes (2) | No (1)  

milan   8 years AGO

Let rohan's work be' A '
similarly suraj be' B' and mahesh be' C'
A+B+B+C+C+A = 1/(12+15+20)
2(A+B+C) = 12/60
2(A+B+C) = 1/5
(A+B+C) = 1/10
HENCE, rohan suraj and mahesh will finish it together in 10 days.

Like? Yes (3) | No (2)  

venkata gowtham   8 years AGO

lcm of 12,15,20=60
rohan do 2parts of 60suraj do 3parts of 60 and mahesh do 1 part of 60 per day respectively
al together gives 10daysto complete 60 parts

Like? Yes | No   

Nitin Garg   8 years AGO

1/x+1/y=1/12;
1/y+1/z=1/20;
1/x+1/z=1/15;

adding them
2/x+2/y+2z= 1/5;
so
1/x+1/y+1/z= 1/10;

Like? Yes (1) | No (1)  

RISHABH   8 years AGO

Let the total unit of work be 60 units.
Rohan + Suraj = 5 units/day
Suraj + Mahesh = 4 units/day
Mahesh + Rohan = 3 units/day
So, 2 (Rohan+ Suraj+ Mahesh) =12 units/day
=>Rohan + Suraj+ Mahesh= 6 units/day
So, no. of days require to complete a work of 60 units
= 60/6 = 10days

Like? Yes | No   

Abhishek Panday   8 years AGO

R+S 1 day work = 1/12
s+M 1 day work = 1/15
M+R 1day work = 1/20
2(R+S+M) 1 day work = 1/12+1/15+1/20 =12/60 =1/5
R+S+M 1day work = 1/10
total day for R+S+M =10

Like? Yes (1) | No (1)  

Akhila Dumpala   8 years AGO

find the LCM of 12,15,20. you will get it as 60.
now divide lcm with number of days they do the work. i.e,
Rohan and suresh completed the work in 12 days. it means that they perform 60/12=5 units of work each day. likewise suresh and Mohan perform 4 units of work each day and Rohan and Mohan perform 3 units of work each day. Add all the units of work they perform each day you will get it as 12 units per day. But each person is repeated twice hence divide the total with 2 now you will get all the 3 persons combined work as 6 units per day. if they perform 6 units in 1 day then in how many days 60 units of work will be done i.e, calculated as 60/6=10 days
6 units --> 1 day
60 units --> ? days
x=1*60/6 = 10 days.
hence answer is 10 days

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Mohan   8 years AGO

Rohan = x, suraj = y, mahesh =z,
12(x+y)=100%
x+y/day=8.33%
y+z/day=6.66%
z+x/day=5%

solve the three equations
x+y+z/day=10%
they need 10 days to complete 100%

Like? Yes | No   

Abhash Kumar   8 years AGO

We see that 2(a+b+c) can do the work in 12*15*20/12*15+12*20+15*20 =5 days. Therefore a+b+c can do the work in 5*2=10 days.

Like? Yes (1) | No (1)  

DEVANSH SUBNANI   8 years AGO

Rohit and Suraj's 1 day work=1/12
Suraj and Mahesh 1 day work=1/15
Mahesh and Rohan's 1 day work=1/20
Add all
(2Suraj +2Mahesh+2Rohan) one day work=(1/12+1/15+1/20)=1/5
(Suraj+Mahesh+Rohan)one day work=1/10
Therefore,they can together finish the work in 10 days.

Like? Yes (1) | No (1)  

Harshit   8 years AGO

(1/12 + 1/15 + 1/20) / 2 = 1/10

1/(1/10) = 10 days

Option 2.

Like? Yes | No (1)  

sanjeet kumar   8 years AGO

2*(sum of 1' days work of all) = 1/5
Together they can finish = 10 days

Like? Yes | No (1)  

Mukund Manohar   8 years AGO

{(R+S) + (S+M) + (M+R)}'s 1 day's work = (1/12 + 1/15 + 1/20)
= 1/5
=> 2(R+S+M)'s 1 day's work = 1/5
=> (R+S+M)'s 1 day's work = 1/10
They will finish it together in 10 days

Like? Yes | No (1)  

Gokul Krishnan   8 years AGO

A+B+C=(2*12*15*20)/((12*15)+(15*20)+(12*20))
=120/12
=10

Like? Yes (1) | No (2)  

Nikita Singhal   8 years AGO

let total work = 60 units
rohan and suraj can do 5 units of work in 1 day (60/12)
suraj and Mahesh can do 4 units of work in 1 day (60/15)
Mahesh and rohan can do 3 units of work in 1 day (60/20)

adding all three
2 (rohan+suraj+Mahesh) can do 12 (5+4+3) units of work in 1 day
rohan+suraj+Mahesh can do 6 units of work in 1 day.

they can together complete the work in 10 days [total work(60)/work per day (6)]

Like? Yes | No (1)  

mohan   8 years AGO

2(a+b+c) 1day work =(1/12)+(1/15)+(1/20)=12/60*2=1/10 units in 1 day ....so total 10 days to complete the work

Like? Yes | No (1)  

Lakshmipathi   8 years AGO

one day work=1/12+1/15+1/20
lcm=60
2(a+b+c)=5+4+3/60
1/10
total work=10 days

Like? Yes | No (1)  

Vijeta    8 years AGO

All the 3 complete their work in 1/12+1/15+1/20 .I.e 1/5.. This if put twice work so 10 days if all three work together

Like? Yes | No (1)  

Anusha Reddy   8 years AGO

R+S=1/12
S+M=1/15
M+R=1/20
consider R=1/12-S
M=1/15-S
put these R and M values in M+R=1/20
then We get S value S=1/20
then put S value in Above two equations we get R=1/30 and M value= 1/60
Finally all worked together R+S+M
1/30+1/20+1/60=6/60=1/10
Answer is 10 days

Like? Yes | No (1)  

kakadiya denish   8 years AGO

Here 12*r + 12*s = 1
15*s + 15*m = 1
20*m + 20*r = 1
so,
R + s= 1/12
s+ m = 1/15
m + r = 1/20
By adding all equations,
2(r+m+s) = 1/12 + 1/15 + 1/20

From this we get
r + m + s =1/10
So
10*(r + m + s) = 1
From above equation,
We can conclude that
All will take 10 hours to complete full work
So answer is 2) = 10

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