CAT 2022 Slot 2 QA Question & Solution
Question
Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is
Solution
Let the time taken by Anu, Tanu and Manu be 5x, 8x and 10x hours.
Total work = LCM(5x, 8x, 10x) = 40x
Anu can complete 8 units in one hour
Tanu can complete 5 units in one hour
Manu can complete 4 units in one hour
It is given, three of them together can complete in 32 hours.
32(8 + 5 + 4) = 40x
x = $\frac{68}{5}$
It is given,
Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day, i.e. 36 + 4 = 40 hours
40(8 + 5) + y(4) = 40x
4y = 24
y = 6
Manu alone will complete the remaining work in 6 hours.