Arun Sharma Solutions for Exercise 2: Level of Difficulty

X takes 4 days to complete one-third of a job, Y takes $3$ days to complete one-sixth of the same work and Z takes$5$ days to complete half the job. If all of them work together for $3$ days and X and Z quit, how long will it take for Y to complete the remaining work done?

A completes $2/3$of a certain job in 6 days. B can complete $1/3$ of the same job in 8 days and C can complete $3/4$ of the work in $12$ days. All of them work together for $4$ days and then A and C quit. How long will it take for B to complete the remaining work alone?

Three diggers dug a ditch of $324$m deep in six days working simultaneously. During one shift, the third digger digs as many metres more than the second as the second digs more than the first. The third digger’s work in $10$days is equal to the first digger’s work in $14$days. How many metres does the first digger dig per shift?

A, B and C working together completed a job in $10$days. However, C only worked for the first three days when $37/100$ of the job was done. Also, the work done by A in$5$ days is equal to the work done by B in $4$ days. How many days would be required by the fastest worker to complete the entire work?

A and B completed a work together in 5 days. Had A worked at twice the speed and B at half the speed, it would have taken them four days to complete the job. How much time would it take for A alone to do the work? 

Two typists of varying skills can do a job in $6$minutes if they work together. If the first typist typed alone for 4 minutes and then the second typist typed alone for $6$minutes, they would be left with $1/5$ of the whole work. How many minutes would it take the slower typist to complete the typing job working alone? 

Three cooks have to make $80$idlis. They are known to make $20$pieces every minute working together. The first cook began working alone and made $20$pieces having worked for some time more than three minutes. The remaining part of the work was done by the second and the third cook working together. It took a total of $8$minutes to complete the $80$idlis. How many minutes would it take the first cook alone to cook $160$idlis for a marriage party the next day? 

Mini and Vinay are quiz masters preparing for a quiz. In $x \mathrm{minutes}$, Mini makes $y$ questions more than Vinay. If it were possible to reduce the time needed by each to make a question by two minutes, then in $x \mathrm{minutes}$ Mini would make $2y$ questions more than Vinay. How many questions does Mini make in $x \mathrm{minutes}$?