Question

Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill it in 7 hours. The number of hours taken by C alone to fill the cistern, is:

Answer 1

Answer:

Step-by-step explanation:

A B C together fill cistern in 6h  

so in 1hr  ABC fill 16th of cistern

so in 2 hrs  1/3rd of cistern will be filled when ABC are together  

so   A B  will fill the remaining 23rd of cistern in 8hrs

so in 1hr AB will fill 2(3∗8)th  of the cistern

so in 1hr AB will fill 112th  of the cistern

let C takes x hours to fill the tank

then in 1hr C will fill 1/xth part of cistern

now cistern filled in 1hr by ABC = cistern filled by AB in 1hr + cistern filled     by C in 1hr

so  

1/6=1/12+1/x

1/x=1/6−1/12

1/x=8/48−4/48

1/x=4/48

1/x=1/12

so x = 12

Answer 2

Answer:

14

Step-by-step explanation:

A+B+C - 6hrs

2hrs work of (A+B+C) - 2/6 =1/3

REMAINING WORK = 1-1/3 =2/3

REMAINING IS COMPLETED BY (A+B)

2/3 ---------- 7HRS

1 ------------- ?

(A+B) COMPLETES THE TOTAL WORK IN 21/2 HRS

1HR WORK OF (A+B) IS ---------2/21

1HR WORK OF (A+B+C) IS -----1/6

(A+B+C)-(A+B)= C's one day work === 3/42 =1/14

therefore c completes the whole work in 14days