Time and work - 2 || Quantitative Aptitude || CAT 2021 || 20 April (App update required to attempt this test)

A and B can complete a piece of work in 12 days and 18 days respectively. If they work on alternate days starting from B, then what fraction of work will be completed in first 13 days?

Rani and Lakshmi can type ten identical books in 25 and 20 days respectively. If Rani, Lakshmi and Veena, together, undertake the work of typing the ten books for a sum of Rs.6000, and complete the work in ten days, find Veena’s share (in Rs.)

Three friends A, B and C can together complete a work in 8 days. If C refused to work with them, then A and B together can complete the work in 10 days and A alone can complete the work in 16 days. It was decided that A and C will together complete 70% of the work and the rest will be completed by B alone. The total time taken by them to complete the work is:

12 men can complete a work in 32 days while 64 women can complete the same work in 12 days. Sixteen men and sixteen women started working and worked for twelve days. How many additional men are required after that to complete the remaining work in 2 days. (TITA)

Abhinav has been growing two types of bacteria P and Q in two different enclosures on a particular day. P bacteria had a starting population of 2, while Q Bacteria had a starting population of 8. However, P bacteria starts growing five hours before the Q bacteria starts growing. On the same day at 8 p.m., Abhinav checks the enclosures and finds that the two types of bacteria have the same population. If the population of P doubles every hour, but the population of Q is quadrupled every hour, at what time did he start growing Q?

A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

A boss can do a job in two days if his four employees A, B, C and D are all present. The efficiency of each gets reduced to  throughout the work if as A,B,C and D remain absent for the entire work respectively. Either A or B or C or D can remain absent for the entire work and if anyone stays absent, all other 3 are bound to continue till the entire work is done without getting absent for any day. Also, the boss finishes his work exactly in integral number of days. If the efficiency of all the employees is equal and Boss only guides the employees in work but do not contribute in job assigned to them, which of the following employee cannot be absent for the entire work?

Ashu starts work at his maximum efficiency rate; but afterwards the rate at which he works follows a cyclic pattern. Every two hours, it reduces by half but after 8 hours, it comes back to its maximum level. He can complete a job in 602 hours at his maximum rate. How many hours would he take to complete the job if his rate follows the cyclic pattern?

John gets Rs 57 per hour of regular work and Rs 114 per hour of overtime work. He works altogether 172 hours and his income from overtime hours is 15% of his income from regular hours. Then, for how many hours did he work overtime?