Time And Work Ques 44
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?
(1) $2: 5$
(2) $2: 7$
(3) $3: 7$
(4) $1: 5$
(5) $3: 5$
(IBPS Bank PO/MT CWE 17.06.2012)
Show Answer
Correct Answer: (4)
Solution: (4)
$(A+B)$ ’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 $=\frac{13}{240}$
$\therefore$ A’s 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 $=48: 240$ or $1: 5$
BETA
