Question

23. To do a certain piece of work, B would take three times as long as A and C together, and C twice a
long as A and B together. The three men together can complete the work in 10 days. How long would
A, B and C separately take to complete the work in days)?
(a) 24, 40, 30
(b) 20, 30, 40
(c) 12, 18, 24
(d) 15, 20, 25​

Answer 1

Answer:

(a) 24,40,30

Step-by-step explanation:

Given,

To do a certain piece of work, B would take three times as long as A and C together,

B=2(A+C)

B/(A+C)=3/1

As they are talking efficiency ,time will be the reciprocal of efficiency then,

B/(A+C)=1/3   ------ (1)

and C twice a  long as A and B together.

C=2(A+B)

C/(A+B)=2/1 is efficiency then time is

C/(A+B)=1/2    -----(2)

The three men together can complete the work in 10 days.

A+B+C=1/10 days----(3)

A+C=1/10-B

substitute A+C in Eq(1)

B/(1/10-B)=1/3

3B=(1-10B)/10

30B=1-10B

40B=1

B=1/40 days

from Eq(3) we can write (A+B)=1/10-C

substitute A+B in Eq (2)

C/(1/10)-C=1/2

2C=(1-10C)/10

20C=1-10C

30C=1

C=1/30 days

fromEq(3),

A=1/10-B-C

A=1/10-1/40-1/30

A=12-3-4/120

A=5/120

A=1/24