Question

Q1.A and B can do a work in 8 days ,B and C can do the same work in 12 days. A , B, C together can finish it in 6days. A and C together will do it in ​?

Answer 1

Explanation:

Given

A and B can do work in 8 days.

B and C can do work in 12 days

A,B,C can do work together in 6 days.

To find

A and C will complete work in how many day

$\sf\huge \mathbb{\underline{\underline{{Solution}}}} </p><p>Solution$

Since A and B can do work in 8 days

Then, Equation becomes : A+B= 8

➙(A+B)'s one day work = 1/8

B and C can do work in 12 days

Then Equation becomes : B+C= 12

➙(B+C)'s one day work = 1/12

A,B,C together can finish the work in 6 days

Then , Equation becomes : A+B+C= 6

➙(A+B+C)'s one day work = 1/6

Then (A+B) and (B+C) can do work => 1/8+1/12 = 5/24

=> A+B+B+C = 5/24

=> A+2B+C = 5/24------(1)

=>A+B+C= 1/6---------(2)

Solving equation 1 and 2

➙A+2B+C= 5/24

➙A+B+C= 1/6

Substract Equation 2 from 1

➙ A+2B+C-(A+B+C)= 5/24-1/6

➙A+2B+C-A-B-C= 5-4/24

➙B= 1/24----(3)

Put B's value into this equation

➙A+B+C= 1/6

➙A+1/24+C= 1/6

➙A+C= 1/6-1/24

➙A+C= 4-1/24

➙A+C= 3/24=1/8

Therefore,A and C together can finish work in 8 days.