PRACTICE QUESTIONS COMPETITION WING

$P, Q$ and $R$ work together to complete a piece of work in $x$ days. $P$ and $R$ take $20$ days and $30$ days, respectively, to complete the work. $Q$ is faster than $R$ and slower than $P$. If $x$ is an integer, then how many values can it take?

$P, Q$ and $R$ can do a piece of work in $18$ days, $36$ days and $54$ days respectively. They start the work together but $Q$ and $R$ leave $1$ day and $5$days respectively, before the completion of work. In how many days has the work been completed ?

Pipes $A, B$ and $C$ can fill a tank in $12 \min$, $24 \min$ and $36 \min$, respectively. Pipes $D$ and $E$ can empty the full tank in $18 \min$ and $72 \min$, respectively. If all of them are opened simultaneously, then find the time taken to fill the empty tank.

The following are the steps involved in solving the above problem. Arrange them in sequential order.

(A) $\frac{11}{72}-\frac{5}{72}=\frac{6}{72}=\frac{1}{12}$

(B) The work done by $5$ pipes in $1 \min =\left(\frac{1}{12}+\frac{1}{24}+\frac{1}{36}\right)-\left(\frac{1}{18}+\frac{1}{72}\right)$

(C) $\left(\frac{6+3+2}{72}\right)-\left(\frac{4+1}{72}\right)$

(D) The part of tank filled by $A, B$ and $C$ in $1 \min$ is $\frac{1}{12}, \frac{1}{24}$ and $\frac{1}{36}$ respectively.

The part of the tank emptied by $D$ and $E$ in $1 \min$ is $\frac{1}{18}$ and $\frac{1}{72}$ respectively.

$X, Y$ and $Z$ can complete a job in $24$ days, $32$ days and $48$ days respectively. They worked together and earned a total of $₹ x$.Find the ratio of their shares.

$P$ and $Q$ can complete a job in $6$ days and $7$ days, respectively. They worked together and earned a total of $₹780$. Find $P\text{'}s$ share in this amount. (in$₹$)

$M$ and $N$ can complete a job in $120$ days and $180$ days, respectively. $M$ started the job and after $60$ days $N$ joined $M$ and they completed the remaining part of the job working together. In how many days was the job completed?

$B$ can do a job twice as fast as $A$ and half as fast as $C$. $A, B$ and $C$ together take $16$ days to complete it. In many days can $C$ alone complete it?

$10$ boys or $20$ girls can complete a job in $10$days, then in how many days can a boy and a girl complete it?