Question

A, B, and C together can finish a place of work in 12 days. A and C together work twice as much as B, A and B together work thrice as much as C. In what time ( day ) could each do it separately

• A. 144/5, 36, 48
• B. 36, 48, 144/5
• C. 48, 144/5, 36
• D. none of these

Answer 1

The correct option is A 144/5, 36, 48

Let A's 1 day work = a

B's 1 day work = b

C's 1 day work = c

$\therefore A+B+C=\frac{1}{12}$ ...(1)

$A+C=2B$ ...(2)

$A+B=3C$ ...(3)

From(2)

$A=2B-C$ ...(4)

from (3)

$A=3C-B$ ...(5)

comparing (4) and (5)

$2B-C-3C-B$

$3B=4C$

$B=\frac{4}{3}C$ ...(6)

putting in (5)

$A=BC-\frac{4C}{3}$

$A=\frac{5C}{3}$ ...(7)

putting (6) and (7) in (1)

$\frac{5C}{3}+\frac{4C}{3}+C=\frac{1}{12}$

$\frac{12C}{3}=\frac{1}{12}$

$C=\frac{1}{48}$

$\therefore A=\frac{5}{3}\times \frac{1}{48}=\frac{5}{144}$

$B=\frac{4}{3}\times \frac{1}{48}=\frac{1}{36}$

$\therefore$ A finishes in $\frac{144}{5}$ days

B finishes in 36 days

C finishes in 48 days