Aptitude - Time and Work - Discussion

24. 

A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :

[A]. 4 days
[B]. 6 days
[C]. 8 days
[D]. 18 days

Answer: Option A

Explanation:

Ratio of rates of working of A and B = 2 : 1.

So, ratio of times taken = 1 : 2.

B's 1 day's work = 1 .
12

Therefore A's 1 day's work = 1 ; (2 times of B's work)
6

(A + B)'s 1 day's work = ( 1 + 1 ) = 3 = 1 .
6 12 12 4

So, A and B together can finish the work in 4 days.


Paandu said: (Jan 26, 2011)  
Why we are ratio this problem and ratio of times taken = 1:2 ?

Ghousia said: (Mar 5, 2011)  
simplest method:
A is twice of B then B=2A
B completes work in=12
then 2A=12=>A=6
A's 1 day work=1/6, B's 1 day work=1/12
(A+B)'s 1 day work=(1/6+1/12)=3/12=1/4
now (A+B) together finish work in 4days

Arun Pandian said: (Jul 8, 2011)  
SHORT CUT METHOD:
let x=2(bcz A is twice as fast as B)
n=12(bcz B completes the work in 12 days)
use the formula:A&B together do the work in p days as follows
p=n/x+1
=12/3
=4days

Umeshprasad said: (Nov 19, 2011)  
Let A's 1 day work is x
B's 1 day work is 1/12
from question a is twice as fast as B
so A=2B------------(1)
x=2*1/12=>1/6
which is one day work of A
combine one day work of A and B is (1/6)+(1/12)
which will give u 1/4
so the entire work they will finish in 4 day.

Deepa said: (Feb 17, 2012)  
B'S one day work=1/12
A'S one day work=2(1/12)=1/6
(A+B) one day work=(1/12)+(1/6)=1/4
hence A and B together complete the work in 4 days

Kapil said: (Feb 20, 2012)  
Simple : A 's twice ie Half of B. . .So B is 1/12 thn Frm tis A is 1/12. . .thn A+B we get t Ans. . .

Omkar said: (Sep 27, 2013)  
A = 2B.

Hence,

A+B = 2B + B

i.e. as good as three Bs working together.

B completes in 12 Days,

3B will take 1/3rd of the time i.e. 12/3 = 4.

Atul1487 said: (Apr 29, 2014)  
Simple method without any rubbish ratio.
Suppose B completes 1 work in x days.

So B completed work in 1 day = 1/x.............1.

Now A completes 1 work = x/2 (Cz A is twice faster than B).

So A completed work in 1 day = 2/x.............2.

Together their Work = 1/x + 2 /x.
Given x = 12.

So,
Together their Work = 1/12 + 2 /12.

== 1/12 + 1/6.
==1/4 or 4 days.

No ratio - nothing complicated.

Swati said: (Oct 1, 2014)  
SHORTCUT:

A is twice efficient as B that means If B takes 12 days then A will take 6 days.
Now both are working together. So definitely together they'll take less than 6 days. ONLY option less than 6 days is Option A i.e. 4 days.

Aravind_Appu said: (Mar 17, 2015)  
A = 2b------(1).
B = 1/12------(2).

1 sub in 2.

A = 2(1/12).
A = 1/6.

Total work is done TH = A+B.

TH = (1/6+1/12).

= (12+6)/(6*12).
= (18/72).
= 1/4.
= 4 day exactly.

Deepa said: (May 30, 2015)  
A:B = 1:2.

B can complete a work in 12 days.

Let A can complete in X days.

X:12 = 1:2.
X = 1*12/2.
X = 6 i.e, A = 6.

(A+B) 1 day work = 1/6+1/12 = 1/4.

So, A and B finish work in 4 days.

Inna Reddy Chilakala said: (Feb 9, 2016)  
A : B = 2 : 1 (work).

B = 12.

A can finish work 1 --- 12.

2 ---- 6.

A+B = 12*6/12+6 = 4.

Kashish said: (Jun 21, 2016)  
More easy solution Guys.

Let assume that B take X time, so A will take 2X.

So now there 1 Days work will 1/x + 2/x = 3/x.

Now from question, they work for 12 days,

3/x = 12.
x = 3/12.
x = 4 ->Answer.

Sudhanshu said: (Dec 25, 2016)  
T --------- W
B --------- 1 1/12
A ---------1 1/6

If A+B work
W --------- T( days)
1/4 --------- 1/1/4.

It comes 4days.

Sudhanshu said: (Dec 25, 2016)  
T --------- W
B --------- 1 1/12
A ---------1 1/6

If A+B work
W --------- T( days)
1/4 --------- 1/1/4.

It comes 4days.

Vaishnavi Kokate said: (Feb 2, 2017)  
Let,
A = 20
B = 10 because A works twice as fast as B.

Total work, B = 10 * 12=120 because B completes his work in 12 days.
so A + B/total work.
120/30 = 4 days.

Arnab said: (May 13, 2017)  
A works twice as fast as B means,

The efficiency of A : B = 2:1 (efficiency means per day work),
A does in 1 day 2 units work.
B does in 1 day 1 unit work.
(A+B) together do in 1 day = 3 units work.

Total work = 1* 12 = 12 units (as per question B can complete a work in 12 days).

(A+B) can do together = 12/ 3 days = 4 days. (Ans.)

Amrit said: (Jul 18, 2018)  
suppose B =x;
and A works twice =2x,
then the total amount of work is;
2x+x=12;
3x=12,
x = 4.

Rajat Pundir said: (Sep 17, 2018)  
a/b=2/1.
Now using the ratio method.
1/12=1/3*(a+b).
1/4=a+b.
Hence 4 days.

Ashish said: (Nov 1, 2018)  
what is 1:2 here?

Veer said: (Mar 16, 2020)  
The easiest way:

A : B = 2 : 1 (work).
B = 12.

A can finish work 1 --- 12.
2 ---- 6.

A+B = 12*6/12+6 = 4.

Manzoor said: (Jul 30, 2020)  
No @Veer

According to me, the solution is;
2A=B in time.
There, the efficiency is inversely proportional to time.
Efficiency of A:B = 1:2

Total work is done by B = No of day's * efficiency
= 12*2 = 24.

If together done the same work= 24รท3.
= 8 days.

Please correct me, If I am wrong.

Uma said: (Jan 4, 2021)  
A=x, B = 2x.
1/x+1/2x = 1/12,
3/2x = 1/12,
3/6 = 2, x = 2.
so, B = 2x, 2 * 2 = 4.

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