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A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10 22 Oct 2017, 19:34
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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5% (low)

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86% (01:51) correct 14% (02:18) wrong based on 284 sessions

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A can do \(\frac{1}{3}\) of the work in 5 days and B can do \(\frac{2}{5}\) of the work in 10 days. In how many days both A and B together can do the work?

A) 7\(\frac{3}{4}\)

B) 8\(\frac{4}{5}\)

C) 9\(\frac{3}{8}\)

D) 10

E) 12
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C
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A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10 23 Oct 2017, 00:10
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varun4s
A can do \(\frac{1}{3}\) of the work in 5 days and B can do \(\frac{2}{5}\) of the work in 10 days. In how many days both A and B together can do the work?

A) 7\(\frac{3}{4}\)

B) 8\(\frac{4}{5}\)

C) 9\(\frac{3}{8}\)

D) 10

E) 12
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This approach looks time-consuming. It isn't. Find and add rates. Work is 1; flip the rate to get the number of days it would take A and B, working together, to finish.

RATES: To find rates, use \(\frac{Work}{time} = rate\)

A's rate, in \(\frac{Work}{days}\):
\(\frac{(\frac{1}{3})}{5}=(\frac{1}{3} * \frac{1}{5})=\frac{1}{15}\)

B's rate:
\(\frac{(\frac{2}{5})}{10}=(\frac{2}{5} * \frac{1}{10})=\frac{2}{50}=\frac{1}{25}\)

Add rates of A, \(\frac{1}{15}\), and B, \(\frac{1}{25}\), with LCM of 75.
COMBINED RATE of A and B:

\((\frac{5}{75} + \frac{3}{75}) = \frac{8}{75}\)

TIME: How many days does it take them, working together, to finish the job?
Job = 1
When work is 1, rate and time are inversely proportional.

Invert the combined rate, \(\frac{8}{75}\), to get the time: \(\frac{75}{8} = 9\frac{3}{8}\) days, OR

\(\frac{Work}{Rate} = time\)

\(\frac{1}{(\frac{8}{75})}= 1 * \frac{75}{8} =9\frac{3}{8}\)

Answer C
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A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10 26 Oct 2017, 15:33
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varun4s
A can do \(\frac{1}{3}\) of the work in 5 days and B can do \(\frac{2}{5}\) of the work in 10 days. In how many days both A and B together can do the work?

A) 7\(\frac{3}{4}\)

B) 8\(\frac{4}{5}\)

C) 9\(\frac{3}{8}\)

D) 10

E) 12
Show more

A’s rate is (1/3)/5 = 1/15 and B’s rate is (2/5)/10 = 2/50 = 1/25.

Their combined rate is 1/15 + 1/25 = 5/75 + 3/75 = 8/75.

Thus, the time it takes the two machines to complete the job is 1/(8/75) = 75/8 = 9 3/8 days.

Answer: C
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A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10 28 Jun 2019, 03:06
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varun4s
A can do \(\frac{1}{3}\) of the work in 5 days and B can do \(\frac{2}{5}\) of the work in 10 days. In how many days both A and B together can do the work?

A) 7\(\frac{3}{4}\)

B) 8\(\frac{4}{5}\)

C) 9\(\frac{3}{8}\)

D) 10

E) 12
Show more

A can do \(\frac{1}{3}\) of the work in 5 days
--> A can do complete work in 3*5 days = 15

B can do \(\frac{2}{5}\) of the work in 10 days
--> B can do complete work in 10*5/2 days = 25

Assume work = LCM(15, 25) = 75 units
Formula: Work done = Rate of work x time
75 = Ra*15 and 75 = Rb*25
--> Rate of A = 5 units/day
--> Rate of B = 3 units/day

Both working together --> Total Rate = 5 + 3 = 8 units/day
--> 75 = 8*t
--> t = 75/8 = 9\(\frac{3}{8}\) days

IMO Option C

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A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10 28 Jun 2019, 03:17
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A can do \(\frac{1}{3}\) of the work in 5 days and B can do \(\frac{2}{5}\) of the work in 10 days. In how many days both A and B together can do the work?

A) 7\(\frac{3}{4}\)

B) 8\(\frac{4}{5}\)

C) 9\(\frac{3}{8}\)

D) 10

E) 12
Show more
Rate of A= 1/(3*5)=1/15
Rate of B=2/(5*10)=1/25
So rate of A+B= 8/75 that is they require 75/8 days = 9 3/8 IMO C

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A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10 29 Aug 2020, 05:44
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A can-do \(\frac{1}{3}\) of the work in 5 days.

For 1 work, A will take 15 days.

In 1 day, A will complete \(\frac{1}{15}\) of the work.

B can do \(\frac{2}{5}\) of the work in 10 days.

For 1 work, B will take 25 days.

In 1 day, B will complete \(\frac{1}{25}\) of the work.

1 day work of (A + B ): \(\frac{1}{15}\) + \(\frac{1}{25}\) = \(\frac{8}{75}\)

1 work will require \(\frac{75}{8}\) days or 9\(\frac{3}{8}\) days.

Answer C
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A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10 29 Aug 2020, 07:23
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A's rate- 1/3 of work in 5 days.
so A can do the complete work in 15 days.
similarly B can do the whole work in 10x(5/2) i.e 25 days
together they can do the work in xy/(x+y) days
i.e 25x15/(25+15) days i.e 75/8 days
i.e 9 whole 3/8 days

ans: C
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A can do 1/3 of the work in 5 days and B can do 2/5 of the work in 10 27 Aug 2023, 17:41
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