Question

7. A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will c take to do it
12
D. 30 days
C 24 day


A. 18 days
71-01-2
-ol
B. 20 days​

Answer 1

Question:-

• A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will c take to do the whole work.

To Find:-

• Find the number of days.

Solution:-

Given ,

• a and b can do work in 3 days.

• b and c can do work in 4 days.

• c and a cab do work in 6 days.

Now ,

We have to find the how many days ' c ' it take to do the work:-

• $\sf \dashrightarrow \ a \: and \: b \: completes \: in \: \bigg ( { \dfrac { 1 } { 3 } \bigg ) }^{ rd } \: of \: work$

• $\sf \dashrightarrow \ b \: and \: c \: completes \: in \: \bigg ( { \dfrac { 1 } { 4 } \bigg ) }^{ th } \: of \: work$

• $\sf \dashrightarrow \ c \: and \: a \: completes \: in \: \bigg ( { \dfrac { 1 } { 6 } \bigg ) }^{ th } \: of \: work$

$\sf \dashrightarrow \ 2( a , b , c ) \: completes \: in \: { \dfrac { 1 } { 3 } }^{ rd } + { \dfrac { 1 } { 4 } }^{ th } + { \dfrac { 1 } { 6 } }^{ th }$

$\sf \dashrightarrow \ a , b , c \: can \: complete \: work \: in \: \dfrac { 3 } { 8 } days$

$\sf \dashrightarrow \ c \: can \: complete \: work \: in \: \dfrac { 3 } { 8 } - \dfrac { 1 } { 3 }$

$\sf \dashrightarrow \ c \:can \: complete \: work \: in \: \dfrac { 9 - 8 } { 24 }$

$\sf \dashrightarrow \ c \: can \: complete \: work \: in \: \dfrac { 1 } { 24 }$

Hence ,

• C can do work in 24 days.