A and B can do a piece of work in 30 days. B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days then B and C leave. How many days more will A take to finish the remaining work?

Open in App

Solution

Answer

Let total work be 120 units (LCM of 30, 24 and 20).

(A+B)'s one day work = 120/30=4 units

(B+C)'s one day work = 120/24=5 units

(C+A)'s one day work = 120/20=6 units

Adding all three equations,
2A+2B+2C=15
2(A+B+C)=15
A+B+C=7.5

SO,
(A+B+C)'s one day work = 7.5 units

A's one day work = (A+B+C)'s one day work-(B+C)'one day work=7.5 - 5 = 2.5 units

In 10 days, all three complete 75 (10×7.5) units of work.
Remaining 45 units can be completed by A in 18 days (at rate of 2.5 units per day).

Suggest Corrections

Similar questions

A

and

B

can do a piece of work in

30

days while

B

and

C

can do the same work in

24

days, and

C

and

A

can do it in

20

days. They all work together for

10

days before

B

and

C

leave. How many more days will

A

take to finish the work?

A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

$A$ and $B$ can do a piece of work in $18$ days. $B$ and $C$ can do it in $24$ days while $C$ and $A$ can finish it in $36$ days. In how many days can $A, B, C$ finish it. if they all work together?

$A$ can finish a piece of work in $15$ days and $B$ can do it in $10$ days. They worked together for $2$ days and then $B$ goes away. In how many days will $A$ finish the remaining work?

Join BYJU'S Learning Program