A can do a certain work in the same time in w | vedclass

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

Question

(C) Let the work done by $A$ in $1$ day be $a$,by $B$ be $b$,and by $C$ be $c$.Given that $A$ does the work in the same time as $B$ and $C$ together,s

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(C) Let the work done by $A$ in $1$ day be $a$,by $B$ be $b$,and by $C$ be $c$.Given that $A$ does the work in the same time as $B$ and $C$ together,so $a = b + c$.Given $(A+B)$'s $1$ day work is $\frac{1}{10}$,so $a + b = \frac{1}{10}$.Given $C$'s $1$ day work is $c = \frac{1}{50}$.Since $a = b + c$,we substitute $b = a - c$ into the equation $a + b = \frac{1}{10}$:$a + (a - c) = \frac{1}{10}$$2a - c = \frac{1}{10}$$2a - \frac{1}{50} = \frac{1}{10}$$2a = \frac{1}{10} + \frac{1}{50} = \frac{5+1}{50} = \frac{6}{50} = \frac{3}{25}$$a = \frac{3}{50}$.Now,find $b$ using $a + b = \frac{1}{10}$:$b = \frac{1}{10} - a = \frac{1}{10} - \frac{3}{50} = \frac{5-3}{50} = \frac{2}{50} = \frac{1}{25}$.Thus,$B$ alone can complete the work in $25$ days.

$A$ can do a certain work in the same time in which $B$ and $C$ together can do it. If $A$ and $B$ together could do it in $10$ days and $C$ alone in $50$ days,then $B$ alone could do the work in (in days)

Similar Questions

$A$ can do a work in $12$ days. When he had worked for $3$ days,$B$ joined him. If they complete the work in $3$ more days,in how many days can $B$ alone finish the work?

$12$ men complete a work in $9$ days. After they have worked for $6$ days,$6$ more men join them. How many days will they take to complete the remaining work?

$3$ men and $2$ women can do a piece of work in $15$ days. $2$ men and $3$ women can do the same work in $18$ days. The number of days to be taken by $1$ man and $1$ woman to do the work is:

If a job is to be completed in $10 \, \text{days}$,it requires $270 \, \text{persons}$. If $180 \, \text{persons}$ take up the same job,they will finish it in (in $\text{days}$):

$A$ is thrice as good a workman as $B$,therefore,$A$ is able to finish a piece of work in $60 \, days$ less than $B$. The time (in $days$) in which they can do it working together is

Vedclass Test Series

Exam Paper Generator

Online Exam Module