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by goyalsau » Sun Dec 05, 2010 8:14 pm
A and B, working together, can build a wall, 221 m long, in 100/9 Days. If they work on alternate days, with A starting the work, it takes 89/4 days to build the same wall. If A and B work together and build a similar wall but of twice the length and earn a total of $1800 for it, then B's share of the earnings is


$750

$800

$1000

$1050

$1100
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by beat_gmat_09 » Sun Dec 05, 2010 9:04 pm
IMO C
A - meters built in 1 day.
B - meters built in 1 day.
1st set - (A+B)*100/9 = 221
2nd set - 11B + (45/4)*A = 221
equating 1 and 2.
B = 1.25 A
B works 25% more than A.
a - amount paid to worker A.
b - amount paid to worker B.
set 3 : a + b = 1800
a + 1.25a = 1800
a = $800
b = $1000
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by diebeatsthegmat » Mon Dec 06, 2010 11:57 am
beat_gmat_09 wrote:IMO C
A - meters built in 1 day.
B - meters built in 1 day.
1st set - (A+B)*100/9 = 221
2nd set - 11B + (45/4)*A = 221
equating 1 and 2.
B = 1.25 A
B works 25% more than A.
a - amount paid to worker A.
b - amount paid to worker B.
set 3 : a + b = 1800
a + 1.25a = 1800
a = $800
b = $1000
can you please explain the second set : 11B + (45/4)*A = 221
?
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by Night reader » Mon Dec 06, 2010 2:13 pm
diebeatsthegmat wrote:
beat_gmat_09 wrote:IMO C
A - meters built in 1 day.
B - meters built in 1 day.
1st set - (A+B)*100/9 = 221
2nd set - 11B + (45/4)*A = 221
equating 1 and 2.
B = 1.25 A
B works 25% more than A.
a - amount paid to worker A.
b - amount paid to worker B.
set 3 : a + b = 1800
a + 1.25a = 1800
a = $800
b = $1000
can you please explain the second set : 11B + (45/4)*A = 221
?
beat_gmat 09: thank you very much for this solution.

to my understanding, alternate days are followed when A starts working on the first day and B starts working on the second day; they interchange each other until the work has been completed.

We have simple equation 1: (A+B)*100/9 = 221
before moving onto equation 2

89/4 = 22 1/4 or 22 days and 1/4th day; A starts and B takes over for 11 days => 11*2=22 days (A then B)
1/4th day is left for A, as he starts the work, therefore =>

11 1/4 *A + 11*B = 221

It makes the first solution clear.
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by beat_gmat_09 » Mon Dec 06, 2010 7:49 pm
diebeatsthegmat wrote:
beat_gmat_09 wrote:IMO C
A - meters built in 1 day by Worker A.
B - meters built in 1 day by Worker B.
1st set - (A+B)*100/9 = 221
2nd set - 11B + (45/4)*A = 221
equating 1 and 2.
B = 1.25 A
B works 25% more than A.
a - amount paid to worker A.
b - amount paid to worker B.
set 3 : a + b = 1800
a + 1.25a = 1800
a = $800
b = $1000
can you please explain the second set : 11B + (45/4)*A = 221
?
A & B both work alternate days, together they work for 89/4 days alternately.
A starts working on the first day. 89/4 is approx 22.somthing so you know that number of days worked is odd number, and as A starts working first , he must end the work, 22/2 = 11, B works for 11 days (you can also try ABAB...)
From this fact itself you now understand that B works more than A to finish the work.
Subtracting 11 days,which B worked from 89/4 you get (89/4) - 11 = 45/4 days for which A worked.
Hence the equation 11B + 45/4 = 221

Solving for the equations you get B = 1.25 A i.e. B works 25% more than A, B should deserve 25% more money than A.
I think the last detail in the stem is not needed to solve. Solving until this time i know that B deserves more money.

So A + 1.2A = $1800
A = $800 and B=$1000
HTH
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