Question: A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
Options:
A) 11 days
B) 13 days
C) $ 20\frac{3}{17}days $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- Ratio of times taken by A and
$ B=100:130=10:13 $
Suppose B takes x days to do the work.
Then, $ 10:13::23:x $
$ \Rightarrow $ $ x=( \frac{23\times 13}{10} ) $
$ \Rightarrow $ $ x=\frac{299}{10} $
A’s 1 days work $ =\frac{1}{23}; $ B’s 1 day’s work $ =\frac{10}{299}. $
$ (A+B)’s $ 1 day’s work $ =( \frac{1}{23}+\frac{10}{299} )=\frac{23}{299}=\frac{1}{13} $ So, A and B together can complete the job in 13 days.
Alternate Method
Let A takes x days to complete the work, then B will take $ x+\frac{30x}{100}=\frac{13x}{10},days $
If they work together, $ (A+B)’s $ 1 day work
$ =\frac{1}{x}+\frac{10}{13x}=\frac{23}{13x} $
Here, $ x=23 $ (as A can complete the work alone in 23 days)
$ \Rightarrow $ $ (A+B)’s $ 1day work $ =\frac{23}{13\times 23}=\frac{1}{13} $
$ \therefore $ Together they can complete the work in 13 days.
BETA
