Directions: Read the following information to answer the question.
Solution:
Let the number of days required by yana to finish the work alone be x days of 8 hrs.
Let the number of days required by urvashi to finish the work alone be y days of 8 hrs.
Let the number of days of overtime by yana and urvashi be p and k respectively.
So,in 12 days yana finishes 12/x+k/2x of work.
In 12 days,urvashi finishes, 12/y+p/2y of work.
So by condition 1, 12/x+12/y+k/2x+p/2y=1....(1)
By condition 2, 15/x+15/y+p/2y=1.....(2)
And,by condition 3, 20/x+20/y+k/2x=1.....(3)
Adding 2 and 3 and subtracting 1 from the result,
1/x+1/y=1/23.
So,if both work normally,they take 23 days.
Directions: Read the following information to answer the question.
(a) If Akshay and John do the work without absence and Akshay digs 6 km, then the work gets completed in a little over 7 days
(b) n = 4/3
(c) If the work gets completed in 7.5 days, when Akshay and John dug without any absence, then Akshay dug 5 km
(d) all of the foregoing
(e) none of the foregoing
Solution: Let W be the amount of work done in digging. Let Akshay, John do W/a and W/b parts of work per day respectively.
Let N, p, q be the number of days in which the work can be done if Akshay, John do the work together without absence, with Akshay absent for 3 days, with John absent for 4 days respectively.
=> NW/a + NW/b = W, (p-3)W/a + pW/b = W and qW/a + (q-4)W/b = W.
Also, pW/b - NW/b = W/10 and qW/a - NW/a = nW/10.
=> p = b/10 + N, q = an/10 + N
=> (b/10 + N-3)/a + (b/10 + N)/b = 1; (na/10 + N)/a + (na/10 + N-4)/b = 1
=> (b/10 - 3)/a + 1/10 + N(1/a + 1/b) = 1 and n/10 + (na/10 - 4)/b + N(1/a+1/b) = 1, but N(1/a + 1/b) = 1
=> b/10 - 3 + a/10 = 0; and n/10(1/a + 1/b) = 4 => n = 4/3 and a+b = 30
Directions: Read the following information to answer the question.
4m and 6w finish in 24 days.
In one day, 4m + 6w = 1/24 of task.
In these questions, just substitute extreme values to get the whole range
If a woman is half as efficient as man
4m + 3m = 1/24 , 7m = 1/24, m = 1/168
6w + 2m = 3m + 2m = 5m, 5m will take 168/5 = 33.6 days
If a woman is as efficient as a man
4m + 6w finish in 24 days
10m finish 1/24 of task in a day
6w + 2m = 8m, 8m will take 240/8= 30 days to finish the task.
So, the range = 30 to 33.6 days. The new team will take 30 to 33.6 days to finish the task.
Directions: Read the following information to answer the question.
A fill pipe can fill a tank in 20 hours, a drain pipe can drain a tank in 30 hours. If a system of n pipes (fill pipes and drain pipes put together) can fill the tank in exactly 5 hours, which of the following are possible values of n (More than one option could be correct)?
3 fill pipes cancel out 2 drain pipes. Plus, you need an additional 4 fill pipes fill the tank in 5 hours. so the answer has to be 5k + 4.
Both 54 and 29 are possible.
Directions: Read the following information to answer the question.
In one minute, A fills (1/30)th of the tank, B fills (1/60)th of the tank, and C fills (1/120)th of the tank.
(B + C) work for 10 minutes, followed by (A + C), which works for “t” minutes, followed by A, which work for 10 minutes. This ensures that the tank gets filled:
10 * (1/60 + 1/120) + t * (1/30 + 1/120) + 10 * (1/30) = 1
10 * (1/40) + t * (1/24) + 10 * (1/30) = 1.
Or, 1/4 + t/24 + 1/3 = 1.
t = 10.
So, the entire tank was filled in 30 mins.