# Aptitude - Time and Work - Discussion

### Discussion :: Time and Work - General Questions (Q.No.21)

21.

A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:

 [A]. 4 days [B]. 6 days [C]. 8 days [D]. 12 days

Explanation:

 Suppose A, B and C take x, x and x days respectively to finish the work. 2 3

 Then, 1 + 2 + 3 = 1 x x x 2 6 = 1 x 2 x = 12.

So, B takes (12/2) = 6 days to finish the work.

 Afua said: (Jun 14, 2010) Where's 6 coming from?

 Ritanjali Natua said: (Jun 28, 2010) 1/x+2/x+3/x=6/x

 Meera said: (Sep 13, 2010) A+B+C's 1 days work is = 1/6. Therefore 2'days work (A+B+C) is=1/6*2=3. B can do the work alone (2*3) =6. So B takes 6 days to finish the work. Is it right method? please anyone tell me.

 Srihari said: (Sep 21, 2010) Hi Meera, It is not right method because A+B+C's 1 day work is only 1/2 not 1/6.

 Ananth said: (Oct 1, 2010) How the total work equation became as (1/x)+(2/x)+(3/x)=1/2 Please explain.

 Kumar said: (Oct 25, 2010) How the work equation became as (1/x)+(2/x)+(3/x)=1/2

 Keyan said: (Nov 11, 2010) How to solve it in 1:2:3 basis?

 Shridhar said: (Nov 26, 2010) As the ques. says, time taken by A is twice that of B and thrice that of C,so this means that A=2*B=3*C ----(eq.1) dividing the whole equation by lcm(1,2,3)=6,we get A/6=B/3=C/2 Now one third of the workdone of B is finished in 2 days therefore complete workdone of B will be finished in 3*2=6 days.

 Lordy said: (Dec 18, 2010) once c the question pls it is mentioned a is twice of b OR thrice of c then how can we divide x,x/2,x/3. if it is mentioned as and then we can decide right?

 Thameem said: (Dec 22, 2010) here is another way of solving given a=2b a=3c a+b=1/2 (work from days) use a's value in the equation 2b+b=1/2 then 3b=1/2 b=1/6 then b can done work alone in 6 days(days from work)

 Student said: (Dec 23, 2010) Hi thameem, hw can we write a+b=1/2? since three members are working is it not a+b+c=1/2.... please explain

 Nayana said: (May 31, 2011) Hi, Can any one exaplain why they have taken x,x/2,x/3, because in the question they have given A takes twice as much as B that means two times more than B but they are dividing it.

 Manasa said: (Jun 11, 2011) @nayana GIVEN: A=2B,A=3C solution: consider A can do work in X days X=2B...B=X/2;X=2C...C=X/3; B can complete work in X/2days,B's 1 day work is 2/X C can complete work in X/3days,C's 1 day work is 3/X A's 1 day work is 1/X. (A+B+C) 1 days work is[(1/X)+(2/X)+(3/X)]=1/2 6/X=1/2 X=12 therefore b can do work in ;B=X/2=12/2=6 days

 Mini said: (Jul 8, 2011) A takes twice much time them B i.e. 2A=B...(i) A takes thrice much time thn C i.e. 3A=C...(ii) It is given dat workin together they can finish in 2 days so A+B+C=1/2 Now put B=2A AND C=3A in this equ... A+B+C=1/2 A+2A+3A=1/2 6A=1/2 A=1/2*6=1/12 Now put the value of A in equ.(i) .i.e B=2A =2*1/12 =1/6 Therefore B takes 6 days to complete the work.

 Divya said: (Jul 10, 2011) A=2B=3C A+B+C=2 ----(EQ.1) WRITING a and c in terms of b, A=2B, C=2B/3 IN EQ.1, 2B+B+2B/3=2 3B+2B/3=2 (9B+2B)/3=2 9B+2B=2*3 11B=6 B=6/11 that means, out of 11 days, b alone completes 6 days of work.

 Md Ali Umar said: (Aug 5, 2011) Hi Mini you are making equ. 2A=B & 3A=C, but so many people a making equ. A=2B & A=3C . Which one s correct, but both one is getting same answer. I'm confussing in this prob. Pls any one describe it ?

 Kiran said: (Nov 30, 2011) B=2A C=3A A+B+C=2days A+2A+3A=2days so,6A=2days A only takes (6*2)=12 days B=2A,so B only takes (12/2)=6days

 Aashish said: (Dec 31, 2011) Can anyone please explain me how 1/x comes? Because, I formed the equation as x+x/2+x/3=2 and got the wrong answer :-(

 Bhaskar said: (Feb 2, 2012) See this solution: Suppose A's 1 day's work= x then B's 1 day's work = 2x,(Since its efficiency is twice of A) C's 1 day's work will be 3x.(Since its efficiency is thrice of A) Now, their combined 1 day's work will be x+2x+3x their combined 2 day's work will be 2(x+2x+3x)=1 gives x=1/12. Since B's 1 day work is 2x =2 *1/12 = 1/6 Hence total days taken by B to complete the same work will be = 6 .

 Jayasree said: (Feb 6, 2012) @nayana Let time taken by B be x then b= x a = 2x which is equal to 3c i.e 2x = 3c c = 2x/3 so a = 2x ; b = x ; c = 2x/3 Dividing each by 2 => x , x/2 , x/3. Hope it is clear.

 Mann Prajapati said: (Apr 2, 2012) Suppose C can complete work in 18 days then A and B can complete the work in 54 and 27 days respectively. Now A's 1 day work is 1/54 and B's 1 day work is 1/27 and C's 1/18. Together 1/54+1/27+1/18=1/9. Work finishes by together in 9 days. Now when work complete in 9 days B's days are 27 so when work complete in 2 days B's days=? 27*2/9=6 days.

 Mariam said: (May 4, 2012) Hai guys, i think mini is correct. from the question we get if B works for 1 hr, A takes 2 hrs to complete the same work i.e.,2A=B

 Mahesh Sarangapani said: (Aug 9, 2012) Suppose A, B and C take x, x/2, x/3 days respectively to finish the work. work done per day by A is 1/x B is 1/(x/2)=2/x C ix 1/(x/3)=3/x And the work done by A, B and C together per day is 1/2 (since work is completed in 2 days) So 1/x + 2/x + 3/x = 1/2 6/x = 1/2 x = 12. Answer : 6

 Faith said: (Mar 14, 2013) My thoughts: Let the time for A to do the job be X. Let the time for B to do the job be 2X (since A takes twice as much time as B). Let the time for B to do the job be 3X (since A takes thrice as much time as C). So it takes all three X+2X+3X = 1/2 (days to finish the job). This gives 6x=1/2. Therefore x=3. Therefore the time taken for B to do the work is 2X. Which is 2*3=6 which is equal to 6days. It takes 3X that is 3*3 for C to do the work. Which is equal 9 days. With the above, you would find out that indeed A takes twice as much time as B and thrice as much time as C. I hope this would suffice.

 Kotha Sravani said: (Jun 21, 2013) Hai friends, Taking the values of A,B,C as x, x/2, x/3. 1/x + 2/x + 3/x = 1/2. On calculating we get, 6/x = 1/2. Therefore, x = 12; On substituting X = 12 in main equation. 1/12 + 2/12+ 3/12 = 1/2. Hence, the value of B = 1/6.

 Ravi said: (Nov 2, 2013) Can anyone please explain me that how these x, x/2, x/3 become 1/x + 2/x + 3/x. Here I don't get is we take 1 day's work of A as 1/x and after that it's taken 2/x + 3/x as B and C's 1 day work but actually after A's 1 day work B's & C's work should be taken as 1/x/2 and 1/x/3. Which becomes x/2 and x/3 So finally it should look like 1/x + x/2 + x/3.

 Apeksha said: (Dec 19, 2013) Why 12 is divided by 2 in last?

 Krishman Varges said: (Dec 20, 2013) This can be solved using physics. Force=Power/time. A, B and C does the same amount of work, hence, force is a constant. The power of three differs. Hence 1/t=f/p where f is a constant and t=2. 1/2=1/x+2/x+3/x.

 Brijesh said: (Jan 12, 2014) Lets assume that A completes the work in 'x' days. B completes the same amount of work in 'x/2' days because A takes twice the time than B. C completes the same amount of work in 'x/3' days because A takes thrice the time than C. Now the work completed by A in one day is '1/x'. Work completed by B in one day is '2/x' Work completed by C in one day is '3/x' All three together can complete the work in '2' days as given in the problem. So the work done by all three together in one day is '1/2'. Hence the equation: '(1/x + 2/x + 3/x) = 1/2'. Evaluating the above equation gives the value 'x=12' which is the number of days taken by A to complete the work. As we know that number of days taken by B complete the work is 'x/2', we substitute the 'x' value. Hence the evaluation '12/2' where 12 is the value of 'x'. HENCE THE TIME REQUIRED BY B TO COMPLETE THE WORK IS 6 DAYS.

 Subhas said: (Aug 10, 2014) A can complete 1 unit/day. B can complete 2 unit/day. C can complete 3 unit/day. Total works complete together by all in 1 days = 6 unit/day. So, they complete in two days = 6X2 = 12 units. So B takes 12/2 = 6 days to complete.

 Rohini said: (Oct 5, 2014) a=2b or a=3c. =>b=a/2 , c=a/3. Let us assume a=x. Then, a b c x x/2 x/3 Therefore., (1/x + 2/x + 3/x) = 1/2. 6/x = 1/2. x = 12. B alone = x/2 = 12/2 = 6.

 Kaviya said: (Jun 28, 2015) How to comes the 1/x+2/x+3/x?

 Wangchuk Drukpa said: (Aug 5, 2015) Let C takes x days to complete the work, then: A, B, C. 3x, 3/2 x and x. Their respective 1 day's work. 1/3x, 3/2x, 1/x now this is equal to 1/2 (as A+B+C takes 2 days to complete the work, thus their 1 day's work would be half). Then we get x=4. Now 3/2 of 4 is 6.

 Khushwinder Pal said: (Aug 10, 2015) Another method. Suppose C = X. C = 2X then B = 3X, A = 6X. Then B = 2X = 2*3 = 6 days. If asked A = 6*3 = 18 days.

 Vidivelli said: (Aug 11, 2015) Let us consider the time taken by B is 2x. So the time taken by A is "twice of B" then A=4x. Similarly if time taken by B is x/2, the time taken by A is (2*x/2) = x; the time taken by C is x/3. So the time taken by A is thrice of C (3* x/3). Hence we get x+x/2+x/3. Since we consider work for one day we take inverse 1/x+2/x+3/x = 1/2.

 G Jogi Rao said: (Sep 30, 2015) Hi @Kiran. If 6A = 2 then A = 3. But you said it A = 12 give proper explanation?

 Dipika said: (Oct 1, 2015) If C takes x days to complete a work A will take 3x days. If B takes y days to complete a work A will take 2y days. But 3x = 2y, so x = 2/3y. As per ques, 1/2y+y+2/3y = 1/2. Therefore y = 6. B takes 6 days to complete the work.

 Naseem Ahmad Saifi said: (Jan 6, 2016) As per given: 2A = B => A = B/2......(1). 3A = C......(2). => 3*B/2 = C......(2) (from 1st A = B/2). (A+B+C)'s do the work in 2 days. So (A+B+C)'s 1 day work is = 1/2. Put the value of A and C from 1st and 2nd. = (B/2+B+3*B/2) 's 1 day work = 1/2. => 6B/2, 1 day work = 1/2. => B's 1 day work = 1/2*2/6 = 1/6. So B complete work in 6 days.

 Punitsw said: (Jan 26, 2016) In simple words: A:B:C = 1:2:3 (Total 6 equivalent to A). Now A, B and C together complete work in 2 days (i.e in 12 man days of A). So if A, B or C do the work alone, the required days would be: A = 12 days. B = 6 days. C = 4 days.

 Mona said: (May 1, 2016) In simple way: A =2B , A = 3C,So ratio will be = A : B : C = 1 : 2 : 3. A = 1 unit/day B = 2unit/day C = 3unit/day A + B + C = 6unit/day. We don't know the total work in units. So, A + B + C = 2 Days TOTAL WORK/DAYS = 6. TOTAL WORK = 6 * 2 = 12 UNITS. So,B = 12/2 = 6 Days.

 Vandana said: (Jun 11, 2016) One query, please answer this question: A, B and C together can finish a piece of work in 12 days, A and C together work twice as much as B, A and B together work thrice as much as C. In what time could each do it separately?

 Makvana Disha said: (Jun 19, 2016) We are also doing this, A's 1 day work = 1/x, B's 1 day work = 2/x, C's 1 day work = 3/x. So, (A + B + C) 's one-day work: = (1/x + 2/x + 3/x). = (1/x + 5x/x ^ 2). = 1/x + 5. = 6x/x = 6 Each of three.

 Rakib said: (Dec 9, 2016) Let A = 12 days(twice than B& thrice than C), B = 6 days, C = 4 days. Working together: (12 * 1/2) = 6 days. Am I Right?

 Raj said: (Dec 28, 2016) 2A = B.......eqn1. 3A = C.......eqn2. A + B + C = 2days A + 2A + C = 2days (from the eqn1), A + 2A + 3A = 2days(from the run2), 6A = 2days , A = 2/6, A = 1/3 days. i.e A takes 3days to work. We have B=2A. B=2(3), B=6. That's B takes 6 days to complete.

 Ravi U S said: (Jan 9, 2017) There are many methods to solve a problem. As I feel Subhas 's method was good, follow it. A can do 1 unit of work in 1 day. B can do 2 unit of work in 1 day. C can do 3 unit of work in 1 day. Totally A+B+C's 1 day's work = 12 units of work. To do 12 units of work B take 6 days.

 Ashok Kumar said: (May 17, 2017) Here is the simple shortcut Given 2A= B Given 3A = C A+B+C=1/2 A+B+3A =1/2 since C=3A 4A+B=1/2 4(B/2) + B =1/2 since 2A=B => A=B/2 6B/2 =1/2 on solve So final B=1/6 i.e B can do the work alone in 6 days.

 Nwbeen said: (May 28, 2017) Where did 1/2 come from?

 Pushpendra said: (Jun 2, 2017) Yes, right @Ravi. Your method of explanation is clear, Thanks @Subhas.

 Raj said: (Jun 13, 2017) @Ravi. Where you get 12 unit work in 1 days and how please explain it?

 Loki said: (Jun 18, 2017) a+2a+3a = 2days. 6a = 2days, a = 1/3(this is total), 3*2 = 6.

 Rajan said: (Jul 5, 2017) Best Solution, Let A take x days to complete the work, Therefore in one day he completes 1/x of the work Thus B will complete the work in x/2 days, Therefore in one day B will complete twice of A's work, i.e 2*(1/x)................(i) Similarly in one day C will complete thrice of A's work, i.e 3*(1/x) Together they take 2 days to complete the work, Therefore in one day they complete 1/2 or 50% of the work,. Thus (work done by A + work done by B + work done by C) in one day = 1/2 or 50% 1/x + 2/x + 3/x = 1/2, (1+2+3)/x = 1/2, 6/x = 1/2, x=12, i.e The days required by A to complete the work. Therefore B will take = x/2 = 12/2 = 6 days......................from eq.(i).

 Bharath Ece said: (Nov 23, 2017) Simple Method. But I explained Elaborate. A is twice time as B => A=2B A is thrice time as c => A=3C therefore; B =A/2 C= A/3 A= A, A=2* (A/2) A taken as X A, B, C X, X/2, X/3 Days Respectively; Rule of Flip or Time to Work 1/x +2//x+3/x =1/2 6/x =1/2 x=12 Asking b Alone. B= x/2 so 12/2 B =6 Days.

 Manish said: (Jan 17, 2018) One day work of a,b&c=1/2 let a's one-day work=x , then b's one day work 2x & c work 3x x+2x+3x=1/2 6x=1/2 x=1/12 b's one day work=2*1/12 =1/6 Therefore total work in 6 days.

 Bulu said: (Apr 25, 2018) @Manish, @Kiran. Thanks for explaining the solution.

 Ajay said: (Jul 8, 2018) Time ratio of A,B,C=6:3:2. Efficiency ratio=1:2:3. It takes 2 days for all of them to complete the work. So, Total work=(1+2+3)*2=12. Time taken by B=12/2 = 6days. Time taken by A=12/1 = 12days. Time taken by C=12/3 = 4days.

 Jatinder said: (Aug 17, 2018) a---12 days . b ----6 days. c --- 4 days. lcm of 12,6,4 = 12. The work done in one day by A- 1 B-2 C-3 then total work done by B in 6 days. 6 is the answer.

 Aadhi said: (Sep 18, 2018) @Ajay. How to find efficiency ratio?

 Rexi said: (Apr 2, 2019) Simply, it is solved by; A=2B ; A=3C. A/2=B ; A/3=C ---> time, 2/A=B; 3/A=C ---> efficiency, 1/A+2/A+3/A = 1/2 ---> A+B+C=1/2. A = 12, B = 6, C = 4.

 Rajshekar said: (Jul 26, 2019) A x. B 2x. C 3x. A+B+B = 1/2, X+2x+3x = 1/2. 6x=1/2. X=1/12. So, be alone =2x = 2 * 1/12 = 1/6 = 6days.

 Manohar said: (Sep 16, 2019) Simply: 6:3:1 = 9 9*2 = 18. 18/3 = 6.