A does half as much work as B in three-fourth of the time. If together

Question

A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it

A. 40 days
B. 35 days
C. 30 days
D. 25 days
E. 20 days

Archit3110 · Accepted Answer

for A given
work 
x/2 = 3/4 * ra
ra = 2x/3
rb= x

given together a & b can do work in 18 days
or say
2x/3 + x= 1/18
5x=1/6
x= 1/30 
days of b = 30 days
IMO C

ScottTargetTestPrep · Answer

We can let n = the number of days it takes B to complete the work by himself. Thus, B’s rate = 1/n and A’s rate = (1/2)/(3n/4) = 4/(6n) = 2/(3n). The sum of their individual rates is 1/18, and we create the equation:

2/(3n) + 1/n = 1/18

Multiplying by 18n, we have:

12 + 18 = n

30 = n

So it takes B 30 days to complete the job by himself.

Answer: C

gracie · Answer

B's time to complete work alone=t
A's rate=(1/2)/(3t/4)=2/3t
18(2/3t+1/t)=1
t=30 days
C

Abedyeasin111 · Answer

How rate is calculated

Posted from my mobile device

warrior1991 · Answer

The work done by A is 1/2 of B. Apply formula W=R*T. Therefore R=W/T.

W=1/2 Work(B) and T=3/4 of Time(B)

R(A)=(1/2(WB))/(3/4)(TB)

R(A)=2/3(RB) because WB/TB= RB by same W=R*T formula.

2/3B+1/B=1/18-----Final equation

Solve and you will get B=30

Hope this helps.

gracie · Answer

let B do 12 units of work per hour
and A do 12/2+6/3=8 units per hour
so B/A rate ratio=12/8=3/2
hence, B completes 3/5 of the house alone in the 18 hours working with A
and completes the remaining 2/5 in 12 hours working alone
18+12=30
C

kingboy2k3 · Answer

Given:
A + B = 1/18

Also Given:
A => B/2 *   3/4T 
B => B *   T

We want to get A in terms of T. Multiply (B/2)*(4/3) and (3/4T)*(4/3)

Now:
A => B(2/3) *   T 
B => B *   T
 
Plug this into our first equation:
B + B(2/3) = 1/18
B = 1/30
B = 30 Days

ScottTargetTestPrep · Answer

If we let n = the total number of days for B to complete the work, the rate of B is 1/n.

The rate of A is (1/2)/(3n/4) = 4/(6n) = 2/(3n)

Since they take 18 days to complete the job:

18/n + (18)  = 1

18/n + 12/n = 1

18 + 12 = n

30 = n

So it takes B 30 days to complete the job.

Answer: C

Shrey9 · Answer

Can you show how to solve this ? I am somehow unable to solve.

2/3B + 1/B = 18
I am taking 
3B as their LCM

2+3/3B = 18

5/3B = 18
which is giving me 5 = 54B, and that's weird..please tell me, what's my mistake ?

ajeng8 · Answer

You have to do the equation in terms of rate, so you set the equation to 1/18 (i.e. the rate), not 18 (the days).

saaiid · Answer

Let B's time = 4, So A's time = 3 
A done half part in 3, so full in 6 
Time : 6:4
Efficiency : 4:6
Work = 10*18= 180
B's time = 180/ 6
30 
Answer : C

Ghoskrp3 · Answer

Let time it takes "A" to complete task be  = A days  
and time it takes "B" to complete task be  = B days

so by the expression, it says A does half as much work as B in three-fourth of the time:
=> in  \frac{3}{4} th of a day, B would have done:  \frac{4}{3B}  amount of work work (as B does  \frac{1}{B}  work in 1 day)
=> A would have done half that => meaning,  \frac{4}{6B}  of work done
 =>  \frac{2}{3B}  
So, A in B's terms takes =   \frac{3B}{2}  days to do that same job as B does in B days

Substituting to find value of B: (as given together they do the work in 18 days) 
  \frac{2}{3B}  +  \frac{1}{B}  =  \frac{1}{18}   
 =>  \frac{2}{3B}  +  \frac{3}{3B}  =  \frac{1}{18}  
 =>  \frac{5}{3B}  =  \frac{1}{18}   
 => B = 30

C. 30 days

Kunal.lost · Answer

I thought of it this way:

If A does half the work in B's 3/4th time, then A would need 3/2B or 1.5B time to finish the entire work. (2*3/4)

Therefore, A's rate would be 1/1.5B and B's rate would be 1/B.

Their combined rate would then be 5/3B.

We're given that working together, they take 18 days to complete the task.

So 1 = 5/3B * 18 (Work done = Rate * Time) which gives B = 30.

KarishmaB Bunuel I'd really appreciate it if you could verify my approach. Thanks

Bunuel · Answer

____________________
Correct.

Srrishti · Answer

let time taken by b to complete work is t , rate of work of b is 1/t .
now time taken by a to complete work is 3t/2 ( 1/2 unit done in 3/4 time of b) , rate of work of b is 2/3t.
now , 
2/3t +1/t =1/18 
t = 30 days which is the answer .

A does half as much work as B in three-fourth of the time. If together

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A does half as much work as B in three-fourth of the time. If together

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