Three men A, B, C working together can do a j | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the time taken by $A, B, C$ working together be $t$ hours.Then $A$ takes $(t+6)$ hours,$B$ takes $(t+1)$ hours,and $C$ takes $2t$ hours.The co

Vedclass · Accepted Answer

$4/3$

Vedclass · Answer

(D) Let the time taken by $A, B, C$ working together be $t$ hours.Then $A$ takes $(t+6)$ hours,$B$ takes $(t+1)$ hours,and $C$ takes $2t$ hours.The combined work rate is $\frac{1}{t+6} + \frac{1}{t+1} + \frac{1}{2t} = \frac{1}{t}$.Subtracting $\frac{1}{2t}$ from both sides: $\frac{1}{t+6} + \frac{1}{t+1} = \frac{1}{2t}$.$\frac{(t+1) + (t+6)}{(t+6)(t+1)} = \frac{1}{2t} \Rightarrow \frac{2t+7}{t^2+7t+6} = \frac{1}{2t}$.$4t^2 + 14t = t^2 + 7t + 6 \Rightarrow 3t^2 + 7t - 6 = 0$.$(3t-2)(t+3) = 0$. Since time must be positive,$t = 2/3$ hours.Now,$A$ takes $2/3 + 6 = 20/3$ hours and $B$ takes $2/3 + 1 = 5/3$ hours.Combined rate of $A$ and $B = \frac{3}{20} + \frac{3}{5} = \frac{3+12}{20} = \frac{15}{20} = 3/4$ work per hour.Time taken by $A$ and $B$ together = $4/3$ hours.

Three men $A, B, C$ working together can do a job in $6$ hours less time than $A$ alone,in $1$ hour less time than $B$ alone,and in one-half the time needed by $C$ when working alone. Then $A$ and $B$ together can do the job in (in hours):

Similar Questions

$A$ certain number of persons can complete a piece of work in $55 \text{ days}$. If there were $6$ persons more,the work could be finished in $11 \text{ days}$ less. How many persons were originally there?

$P$ can complete a work in $12$ days working $8$ hours a day. $Q$ can complete the same work in $8$ days working $10$ hours a day. If both $P$ and $Q$ work together,working $8$ hours a day,in how many days can they complete the work?

$A$ can do a work in $20 \, days$ and $B$ in $40 \, days$. If they work on it together for $5 \, days$,then the fraction of the work that is left is:

$A, B$ and $C$ do a job in $6$ days,$12$ days and $15$ days respectively. After $\frac{1}{8}$ of the work is completed,$C$ leaves the job. The rest of the work is done by $A$ and $B$ together. What is the time taken to finish the remaining work? (in days)

$2$ men and $3$ women can complete a work in $10$ days,while $4$ men can complete it in $10$ days. In how many days will $3$ men and $3$ women complete the work?

Vedclass Test Series

Exam Paper Generator

Online Exam Module