a B तथा C मिलकर किसी काम को a की तुलना में 6 घंटे कम तथा C की तुलना में आधे समय में पूरा करते है तो A तथा B मिलकर कितने दिनों में पूरा करेंगे ?

Options

A. `(2)/(3)` hour
B. `(2)/(3)` hour
C. `(3)/(2)` hour
D. `(4)/(3)`hour

Answer

d

Explanation

(d) Let X is total time time taken by (A+B+C) B
`(A+B+C)/(x)(A)/(x+6)(b)/(x+1)(c) /(2x)`
`{:(time ,1,:,2),( efficiency ,2,:,1):}`
(a+B) 's eficiency =2-1=1
`{:(,A+B,:,C),(eff,1 ,:,1),( days,2x,:,2x):}`
` (A+B)/(2x)=(C)/(2x)`

`2X sqrt((6-x)(1-x))=3x^(2)+7X-6=0`
`x=(2)/(3)`
A alone does `=(2)/(3)+6` =`(20)/(3)` hours ,B alone `""_(3)^(2)1` = ` ""_(3)^(5) ` hrs A+B can do it in `=(4)/(3)` hours
alternate :- Let (A+B+C) can complete comthe work in x hours
time taken by A+(X+6) hours c==2X hours
According to the question , "`(1)/(x) =(1)/(x+6)+(1)/(x+1)+(1)/(2X)`
`(1)/(x)-(1)/(2x)=(1).(x+^6)+(1)/(x+1)`
x=2/3 hours
A=6+2/3=20/3 hours
B=1+2/3=5/3 hours

A+B can do it in `=(4)/(3)` hours