A, B, and C were to be paid in proportion to the part of work they did

Question

A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $720 was the net sum to be paid for the entire work, what was the average daily wage of B?

(A) $144
(B) $90
(C) $60
(D) $54
(E) $48

Kudos for a correct solution.

(A) $144 
(B) $90 
(C) $60 
(D) $54 
(E) $48

Kudos for a correct  solution .

tarangchhabra · Accepted Answer

A & B together worked for 5 days
B can complete the work by himself in 15 days (1/15 of work in one day)
Thus, total work B did = 5*(1/15) = 1/3

Total wage B will get = (1/3)*720 = $240

Thus average wage: 240/5 = $48

shriramvelamuri · Answer

A's one day work= 1/12 and B's one day work= 1/15.

Together, A and B will do 9/60 of work per day-> in 5 days they do 45/60 work=> 3/4 of the work. Remaining 1/4 of the work was done by C.

Now Money

Total work done by A= 5/12. Total work done by B=5/15 and total work done by C= 1/4.

5/12: 5/15: 1/4== 5:4:3.

So average of B= (4/12)*720= 240. ==> Wage per day= 240/5=48$.

Konstantin1983 · Answer

A's work rate is (1/12) and that of B's is (1/15). Together in five days they did (5/12)+(5/15)=3/4. Hence C should finish (1/4) of the remaining part. In money terms A+C got ((720)*(2/3))=480 dollars. Hence 240 is left for B. B's average is (240)*(1/5)=48

PareshGmat · Answer

Rate of A =  \frac{1}{12}

Rate of B =  \frac{1}{15}

Combined rate =  \frac{9}{60}

Work done in 5 days  = \frac{9}{60} * 5 = \frac{45}{60}

Costing for 5 days combined work = \frac{45}{60} * 720 = 540

Work done in 5 days by B = \frac{1}{15} * 5 = \frac{5}{15}

Costing for 5 days for B  = 540 * \frac{5}{15} * \frac{60}{45}= 240

Costing per day for B  = \frac{240}{5} = 48

Answer = E

kaiyuan28935749 · Answer

How do we know how many days C worked, as it sounds like C commenced work  after  the 5 days that A & B worked?

Bunuel · Answer

A and B working together in 5 days completed 5*(1/12 + 1/15) = 45/60 part of the job. Thus, C completed 15/60 th of the job alone. It does not matter in how many days C completed its part of the job because we need only proportion of the job done by A, B and C to determine B's share.

saumyagupta1602 · Answer

Work done by A= 1/12
Work done by B=1/15
Let Total Work done be 60 units (taking LCM 12, 15)
So, Work done by A= 60/12=5 units per day
So, Work done by B=60/15=4 units per day
A & B work together for 5 days, so they complete (5+4)*5= 9*5=45 units and 60-45=15 units is completed by C 
Thus proportion in which A,B and C can draw salary is
A : B : C
5units*5Days: 4units*5 days: 15units*1 day
25 : 20 : 15
5 : 4 : 3
Thus value of B's average wage = 4/(5+4+3)=4/12=1/3= x/720 thus x= 240 and average wage per day for 5 days= 240/5= 48 ; hence, option E

kaiyuan28935749 · Answer

Thanks Bunuel

Posted from my mobile device

DaniyalAlwani · Answer

shriramvelamuri

Can you please explain how you converted:

5/12: 5/15: 1/4==>> 5:4:3

HimanshuSonigara · Answer

Consider work to be 60 units

A can do the work in 12 days i.e. 5 units per day, hence 25 units in 5 days
B can do the same work in 15 days .i.e. 4 units per day, hence 20 units in 5 days

Working together for 5 days A&B complete 45 units in 5 days and remaining 15 units is completed by C.

Now, A did 25 units, B did 20 units and C did 15 units.

Therefore, wage for B is 4/12*720 = $240

Now, 240/5 = $48 per day

effatara · Answer

A lot of information has been provided in the question stem which are not needed to solve this question. The only relevant information needed is B can complete the job by himself in 15 days, he worked for 5 days and the total payment for the job was $720. The correct approach was by  tarangchhabra . Any other approach would involve wasting time unnecessarily to arrive at the same answer.

bumpbot · Answer

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A, B, and C were to be paid in proportion to the part of work they did

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