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 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
Answers
Answer:
B.15mins
Step-by-step explanation:
Say no-1 typist takes x mins to to type the job and no.2 typist takes y mins to type the job
No-1 in 1 min does 1/x of the job
No-2 in 1 min does 1/y of the job
No-1 in 4 mins and no-2 in 6 mins type =(4/x +6/y) of the job
1-(4/x+6/y)=1/5
=>4/x+6/y=4/5 .................................1
when they work together in 1 min, they type= (1/x+1/Y)
in 6 mins they type (1/x+1/y)*6=1 (they do the full job, which is 1)
=>6/x+6/y=1 ..........2
Multiply eq.1 by 6 and eq.2 by 4 and subtracting
24/x+36/y=24/5
24/x+24/y=4
---------------------------------
12/y=4/5
y=15 mins
using value of y in equ.2 , we get x=10mins
hence 2nd typyist is slowest and can finish the job alone in 15 mins.
----: ||ANSWER|| :----
Working efficiency of both typist together,
= 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 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 100/6.66 = 15.01 = 15 minutes.