Two typist of varying skills can do a job in 6 minutes if they work together. If the first typist typed alone for 4 minutes and then the second typist typed alone for 6 minutes, they would be left with $$\frac{1}{5}$$ of the whole work. How many minutes would it take the slower typist to complete the typing job working alone ?
A. 10 minutes
B. 15 minutes
C. 12 minutes
D. 20 minutes
E. 17 minutes
Answer: Option B
Solution (By Examveda Team)
Working efficiency of both typist together, = $$\frac{{100}}{6}$$ = 16.66% per minute Now, let work efficiency of first typist be x and then second typist will be (16.66 - x) First typist typed alone for 4 minutes and second typed alone for 6 minutes and they left with $$\frac{1}{5}$$ (i.e 20%) of job, means they have completed 80% job Now, First Typist typed in 4 minute + Second typed in 6 minutes = 80% 4 × x + 6 × (16.66 - x) = 80% 4x + 100% - 6x = 80% x = 10% First Typist typed 10% per minutes. Then second typed (16.66 - 10) = 6.66% per minute Then, Second typist complete the whole job in $$\frac{{100}}{{6.66}}$$ = 15.01 = 15 minutes.This Question Belongs to Arithmetic Ability >> Time And Work
Let, First typist can type A part / Minute.
Second typist can type B part / minute.
So, 6A+6B = 1 part.....(1)
4A+6B = 1-1/5 part....(2)
Now, (1)-(2) we get,
A = 1/10
Putting the value of A into (1)
B=1/15
So, B can do 1/15 part in 1 minute
B can do 1 part in 15 minutes
Let total work = 60 pages
They both complete the work in 6 minutes
I.e 60/6 = 10 pages per minute
Because it’s given that one typist is fast and one is slower, we can assume that
Fast one will complete 6 page per minute
Slower one will do 4 page per minute
So slower one will take
60/4 = 15 minutes to complete.
(6a+6b)/5=(4a+6b)/4
=>24a+24b=20a+30b
=>4a=6b
=>a/b=3/2
Then (3+2)*5=2*h
=>h=15 minutes
I would recommend the solution process by a different method.
Let the total letter to be typed by both typist be W letters.
A types letter in with speed of A letters/min and B types letter in with speed of B letters/min.
So, total letters typed after 6 mins is A*6 + B*6 = W.
Now, when typed alone A*4 + B*6 = W-W/5
Solving both equation we'll get B = W/15 and A = W/10
So, B*15 = W.
i.e B takes 15 mins to complete total work and A takes 10 min to complete total work.
Let the total letters to be typed by both typist 'A' & 'B' be W letters.
'A' types letter in with speed of A letters/min and 'B' types letter in with speed of B letters/min.
So, total letters typed after 6 mins is A*6 + B*6 = W.
Now, when typed alone A*4 + B*6 = W-W/5
Solving both equations we'll get B = W/15 and A = W/10
So, B*15 = W & A*10 = W
i.e B takes 15 mins to complete the total work and A takes 10 mins to complete the total work.