Time and Work

A began to do a job alone. After 6 days, he was joined by B. They both worked for another 5 days, after which they were joined by C. Three of them completed the work in a further period of 9 days. How long would C take to do the entire work alone, assuming that A and B separately could do the whole work in 36 days and 42 days, respectively?

Directions: Read the information given below carefully and answer the question that follows. (i) A and C together can complete a certain job in 40 days. (ii) B and D together can complete the same job in 80 days. (iii) B alone can complete the same job in 100 days. (iv) A alone can complete the same job in 50 days. Which of the given statements is redundant to find that A alone takes how many days less to complete the job than both C and D together?

P alone can complete a certain job in x days. Q alone can complete the same job in 2x day. R alone can complete the same job in (x + 32) days. Also, P and R together can complete the same job in 12 days. R starts working and works for (x/4) days. After that, P and Q join R to complete the remaining task together. Find the value of (Y + 1/2) days, if Y is the number of days taken by P, Q and R together to complete the remaining task.

A can do a piece of work in 90 days, B can do it in 40 days and C can do in 12 days. They take turns and work for a day each, i.e. on the first day, A works alone; on the second day, B works alone; and on the third day, C works alone. The cycle is repeated till the work is finished. They get $240 for this job. If the wages are divided in proportion to the work each has done, then find the amounts each will get.

Ramos, Karen and Vincent take a contract to do a piece of work. Ramos can do it alone in 10 days. Karen can do it in 20 days and Vincent can do it in 40 days. They work alternately. On the 1^st day, Ramos will do it alone, on the 2^nd day, Karen will do it and on the 3^rd day, Vincent will do it alone, and so on till the work is completed. Find the time taken to complete the work.

A contractor receives weekly payments for work done that he uses for paying wages. His capital, together with the weekly payment, would just enable him to pay 42 men for 52 weeks. If he had 60 men at the same wage, his capital, together with the weekly payment, would just suffice for 13 weeks. How many men can be maintained for 26 weeks?

Kelly and Lelly are two carpenters, they take a contract worth $1008. Kelly, who is more efficient, can finish the job in 6 days, while Lelly can finish it in 12 days. They start working together, but Kelly quits after 2 days. Lelly works alone for 3 days and after that, Kelly is called back and he finishes the remaining work alone. Find the amount that each one gets at the end, assuming that the amount is distributed in the ratio of the amounts of work done by them.

10 skilled men and 5 skilled women can complete a work in 4 days, while 8 skilled men and 10 skilled women can complete the same work in 3 days. The efficiency of unskilled men is 40% less than the efficiency of skilled men and the efficiency of unskilled women is 50% less than the efficiency of skilled women. Quantity I: Time taken to complete the whole work by 4 unskilled men and 1 skilled woman. Quantity II: Time taken to complete the whole work by 5 unskilled women and 1 skilled man.