Type A employees are 100% more productive than type B employees and ty

Question

Type A employees are 100% more productive than type B employees and type B employees are 100% more productive than type C employees. If 30 type A employees need to work for six hours a day, for 50 days to complete a project, how long will it take a team of 80 type B employees and 80 type C employees to complete the same project if they work ten hours a day?

A. 10
B. 15
C. 20
D. 30
E. 60

A. 10
B. 15
C. 20
D. 30
E. 60

darunp · Accepted Answer

since 30 of type A can finish work in (50*6) hours, rate of 30 workers can be written as:

30*A=\frac{1}{6*50}

so rate of work for 1 type A:
 A=\frac{1}{6*50*30}

since
 A = 2*B 
 B = 2*C 
so  A = 4*C

80B = 40A  and  80C = 20A

so combined rate of 80B & 80C would be  \frac{40}{6*50*30}+\frac{20}{6*50*30}=\frac{60}{6*50*30}=\frac{1}{150}

work = rate * time
 1=\frac{1}{150}*(10*d)  where d is the number of days
 d=15

PyjamaScientist · Answer

Option (B)   15 days in my opinion.

Higher productivity means, a person can do more work than the other person. So, type A worker's rate is 4 times that of type C worker and 2 times that of type B worker.

Create work rate equations, and solve.

SaquibHGMATWhiz · Answer

Solution: Productivity can be equivalent to the Rate of work "Type A employees are 100% more productive than type B" means we can write R_A=R_B(1+\frac{100}{100})⇒R_A=2R_B⇒R_B=\frac{R_A}{2} "Type B employees are 100% more productive than type C" means we can write R_B=R_C(1+\frac{100}{100})⇒R_B=2R_C⇒R_C=\frac{R_A}{4} Now, we can make a table for W=nRT as follows: WRT3.png Let us assume 80 type B and 80 type C employees are working 10 hours a day for n days: WRT4.png Thus, we can say 800nR_B+800nR_C=9000R_A ⇒800n(R_B+R_C)=9000R_A ⇒8n(\frac{R_A}{2}+\frac{R_A}{4})=90R_A ⇒\frac{24n}{4}=90 ⇒n=15 Hence the right answer is Option B

hrishika.ag · Answer

Let the productivity of Type C be x.
Then, Type B is 2x and Type A is 4x.

Work done by 30 Type A employees in 6 hours per day for 50 days:
30 employees × 4x × 6 hours × 50 days = 36000x

Combined rate of 80 Type B and 80 Type C employees:
(80 × 2x) + (80 × x) = 240x per hour

Let the number of days they work be d.
Then, total work they do in 10 hours per day for d days = 240x × 10 × d = 2400x × d

Equating both works:
36000x = 2400x × d 
 d = 15

DylanD · Answer

This one was quite challenging for me. Here is the approach I experimented with:
1. Setup a "multiplicative ratio table"
rb = Rate of Type B Employees
   Employee Type 
 # of Employees 
 *(rate) 
 *(time) 
 =(work) 
 
  C 
 80 
 (1/2)*(rb) 
 (10 hr/day)*(t day)

B 
 80 
 (rb) 
 (10 hr/day)*(t day)

A 
 30 
 (2)*(rb) 
 (6 hr/day)*(50 day) 
 1 project

2. Work of (B + C) = (Work of A) = (1 project)
(8 0 )*( rb )*(1 0 )*(t) + (8 0 )*(1/2)*( rb )*(1 0 )*(t) = (3 0 )*(2)*( rb )*(6)*(5 0 )
i) Divide both sides by  common terms  (A pair of 10s and rb)
(8)*(t) + (4)*(t) = (3)*(2)*(6)*(5)
ii) Solve for t
t*(8+4) = (3)*(12)*(5)
t = 3*5 = 15

ANSWER: B

As an exercise in translating the multiplicative ratio table to English and back to math: 
i) MRT -> English
A has three-eights the employees of B or C.
A's rate is twice B's or four times C's. 
A works three-fifths (6/10) the hours per day as B or C.
A completes the same amount of work as B or C in fifty days.

ii) English -> Math
For "B or C" statements, we can   out these values (given a multiplicative relationship)
Work of A = Work of B + Work of C
(3)*(2*rb)*(3)*(50) =  *(1 + (1/2))

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Type A employees are 100% more productive than type B employees and ty

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Employee Type	# of Employees	*(rate)	*(time)	=(work)
C	80	(1/2)*(rb)	(10 hr/day)*(t day)
B	80	(rb)	(10 hr/day)*(t day)
A	30	(2)*(rb)	(6 hr/day)*(50 day)	1 project

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