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WarriorWithin
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Two typists undertake to do a job. The second typist begin working one 22 Nov 2020, 01:37
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85% (hard)

Question Stats:

57% (02:52) correct 43% (02:50) wrong based on 169 sessions

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Two typists undertake to do a job. The second typist begin working one hour after the first. Three hours after the first typist has begun working, there is still (9/20) of the work to be done. When the assignment is completed, it turns out that each typist has done half the work. How many hours would it take each one to do the whole job individually?

A. 12 hours and 8 hours
B. 8 hours and 5.6 hours
C. 10 hours and 8 hours
D. 5 hours and 4 hours
E. 4 hours and 8 hours
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C
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Two typists undertake to do a job. The second typist begin working one 22 Nov 2020, 05:36
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WarriorWithin
Two typists undertake to do a job. The second typist begin working one hour after the first. Three hours after the first typist has begun working, there is still (9/20) of the work to be done. When the assignment is completed, it turns out that each typist has done half the work. How many hours would it take each one to do the whole job individually?

A. 12 hours and 8 hours
B. 8 hours and 5.6 hours
C. 10 hours and 8 hours
D. 5 hours and 4 hours
E. 4 hours and 8 hours
Show more



Let the 1st Typist (A) take x hours and the second typist (B) take y hours.

Work done in 1 hour by A = \(\frac{1}{x}\) and work done in 1 hour by B = \(\frac{1}{y}\)

Now after 3 hours, A has worked for 3 hours and B has worked for 2 hours (starts 1 hour later)

The fraction of work completed by A in 3 hours = \(\frac{3}{x}\) and by B in 2 hours = \(\frac{2}{y}\)


The amount of work completed = \(1 - \frac{9}{20} = \frac{11}{20}\)

So, \(\frac{3}{x} + \frac{2}{y} = \frac{11}{20}\)


At this point, we can use the options to get our answer


Option A: \(\frac{3}{12} + \frac{2}{8} = \frac{1}{4} + \frac{1}{4} = \frac{1}{2}\)


Option B: \(\frac{3}{8} + \frac{2}{5.6} = \frac{3}{8} + \frac{5}{14} = \frac{41}{56}\)


Option C: \(\frac{3}{10} + \frac{2}{8} = \frac{3}{10} + \frac{1}{4} = \frac{11}{20}\)


Option C

Arun Kumar
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Two typists undertake to do a job. The second typist begin working one 22 Nov 2020, 06:40
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WarriorWithin
Two typists undertake to do a job. The second typist begin working one hour after the first. Three hours after the first typist has begun working, there is still (9/20) of the work to be done. When the assignment is completed, it turns out that each typist has done half the work. How many hours would it take each one to do the whole job individually?

A. 12 hours and 8 hours
B. 8 hours and 5.6 hours
C. 10 hours and 8 hours
D. 5 hours and 4 hours
E. 4 hours and 8 hours



Let the 1st Typist (A) take x hours and the second typist (B) take y hours.

Work done in 1 hour by A = \(\frac{1}{x}\) and work done in 1 hour by B = \(\frac{1}{y}\)

Now after 3 hours, A has worked for 3 hours and B has worked for 2 hours (starts 1 hour later)

The fraction of work completed by A in 3 hours = \(\frac{3}{x}\) and by B in 2 hours = \(\frac{2}{y}\)


The amount of work completed = \(1 - \frac{9}{20} = \frac{11}{20}\)

So, \(\frac{3}{x} + \frac{2}{y} = \frac{11}{20}\)


At this point, we can use the options to get our answer


Option A: \(\frac{3}{12} + \frac{2}{8} = \frac{1}{4} + \frac{1}{4} = \frac{1}{2}\)


Option B: \(\frac{3}{8} + \frac{2}{5.6} = \frac{3}{8} + \frac{5}{14} = \frac{41}{56}\)


Option C: \(\frac{3}{10} + \frac{2}{8} = \frac{3}{10} + \frac{1}{4} = \frac{11}{20}\)


Option C

Arun Kumar
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How can we solve this by forming equations with the work data given?
Thanks in advance 😊

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Two typists undertake to do a job. The second typist begin working one 22 Nov 2020, 06:46
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Yadhukrishna
How can we solve this by forming equations with the work data given?
Thanks in advance 😊

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Hi Yadhukrishna


Let the additional hours to complete the work = a hours

Then each fraction of work done by A and B = \(\frac{1}{2}\)

i.e Fraction of work done by A = \(\frac{3 + a}{x} = \frac{1}{2}\). Therefore 2a = x - 6

Fraction of work done by B = \(\frac{2 + a}{y} = \frac{1}{2}\). Therefore 2a = y - 4

Equating x - 6 = y - 4 or x = y + 2


Again using the answer choices, x = 10 and y = 8 satisfy the above equation.

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Two typists undertake to do a job. The second typist begin working one 23 Nov 2020, 20:05
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Two typists undertake to do a job. The second typist begin working one hour after the first. Three hours after the first typist has begun working, there is still (9/20) of the work to be done. When the assignment is completed, it turns out that each typist has done half the work. How many hours would it take each one to do the whole job individually?

A. 12 hours and 8 hours
B. 8 hours and 5.6 hours
C. 10 hours and 8 hours
D. 5 hours and 4 hours
E. 4 hours and 8 hours
Show more

Let the first typist take x hours and second typist take y hours to do the whole job.

So, 3 hours work of first typist and 2 hours work of second typist combined = 11/20

3/x + 2/y = 11/20 …(1)

Also it has been given that finally both have done the same amount of work.

x/2-y/(2 ) = 1 …(2)

From (1) and (2), we get x = 10 hours and y = 8 hours.
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Two typists undertake to do a job. The second typist begin working one 02 Dec 2020, 00:45
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WarriorWithin
Two typists undertake to do a job. The second typist begin working one hour after the first. Three hours after the first typist has begun working, there is still (9/20) of the work to be done. When the assignment is completed, it turns out that each typist has done half the work. How many hours would it take each one to do the whole job individually?

A. 12 hours and 8 hours
B. 8 hours and 5.6 hours
C. 10 hours and 8 hours
D. 5 hours and 4 hours
E. 4 hours and 8 hours

Let the first typist take x hours and second typist take y hours to do the whole job.

So, 3 hours work of first typist and 2 hours work of second typist combined = 11/20

3/x + 2/y = 11/20 …(1)

Also it has been given that finally both have done the same amount of work.

x/2-y/(2 ) = 1 …(2)

From (1) and (2), we get x = 10 hours and y = 8 hours.
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Can you please elaborate this 2nd equation.
I think 2nd equation is enough to solve the question, because difference between (x-y) = 2 and with the help of options we can verify the same
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Two typists undertake to do a job. The second typist begin working one 16 Jan 2024, 09:48
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WarriorWithin
Two typists undertake to do a job. The second typist begin working one hour after the first. Three hours after the first typist has begun working, there is still (9/20) of the work to be done. When the assignment is completed, it turns out that each typist has done half the work. How many hours would it take each one to do the whole job individually?

A. 12 hours and 8 hours
B. 8 hours and 5.6 hours
C. 10 hours and 8 hours
D. 5 hours and 4 hours
E. 4 hours and 8 hours

Let the first typist take x hours and second typist take y hours to do the whole job.

So, 3 hours work of first typist and 2 hours work of second typist combined = 11/20

3/x + 2/y = 11/20 …(1)

Also it has been given that finally both have done the same amount of work.

x/2-y/(2 ) = 1 …(2)

From (1) and (2), we get x = 10 hours and y = 8 hours.


Can you please elaborate this 2nd equation.
I think 2nd equation is enough to solve the question, because difference between (x-y) = 2 and with the help of options we can verify the same
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The question says, when the work is finished, each has done half the amount of work. But the first person takes one extra hour than the second person. Therefore the equation justifies.
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Two typists undertake to do a job. The second typist begin working one 14 Jul 2026, 20:51
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Two typists undertake to do a job. The second typist begin working one 14 Jul 2026, 22:19
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Two typists undertake to do a job. The second typist begin working one hour after the first. Three hours after the first typist has begun working, there is still (9/20) of the work to be done. When the assignment is completed, it turns out that each typist has done half the work. How many hours would it take each one to do the whole job individually?

A. 12 hours and 8 hours
B. 8 hours and 5.6 hours
C. 10 hours and 8 hours
D. 5 hours and 4 hours
E. 4 hours and 8 hours
Show more

Using approximation:

First typist works alone for 1 hr and both work together for 2 hours and they complete 11/20 of the work (a little more than half). Only 9/20 is leftover.
They will take about 2 hours together to complete the rest of the work. So first typist works for 5 hrs to do half the work and second typist works for 4 hrs to do half the work. Hence they will take 10 and 8 hrs respectively for the complete work.

To Confirm: Say there were 20 units of work. If the first typist does 2 units per hour (and hence takes 10 hrs to complete it) and the second typist does 2.5 units per hour (and hence takes 8 hrs to complete it), in first 3 hours, they would do 3*2 + 2*2.5 = 11 units. Leftover would be 9 out of the 20 units. This is exactly what is given. Correct.

Answer (C)
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