Two typists undertake to do a job. The second typist begin working one

Question

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

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

CrackverbalGMAT · Accepted Answer

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

Yadhukrishna · Answer

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

Posted from my mobile device

CrackverbalGMAT · Answer

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.

Arun Kumar

WarriorWithin · Answer

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.

Vallabhm001 · Answer

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

samarpan.g28 · Answer

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

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