Question: A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 40 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone?
Options:
A) 2: 5
B) 2: 7
C) 3: 7
D) 1: 6
E) 3: 5
Show Answer
Answer:
Correct Answer: D
Solution:
- $ (A+B)’s $ 1 day’s work $ =\frac{1}{20} $
$ (B+C)’s $ 1 day’s work $ =\frac{1}{30} $
$ (C+A)’s $ 1 day’s work $ =\frac{1}{40} $
On adding,
$ 2(A+B+C)’s $ 1 day’s work $ =\frac{1}{20}+\frac{1}{30}+\frac{1}{40} $
$ =\frac{6+4+3}{120}=\frac{13}{120} $
$ \therefore $ $ (A+B+C)’s $ 1 day’s work $ =\frac{13}{240} $
$ \therefore $ As 1 day’s work
$ =\frac{13}{240}-\frac{1}{30}=\frac{13-8}{240}=\frac{5}{240}=\frac{1}{48} $
C’s 1 day’s work $ =\frac{13}{240}-\frac{1}{20}=\frac{13-12}{240}=\frac{1}{240} $
$ \therefore $ Required ratio $ =48:240=1:5 $
BETA
