The ones who are crazy enough to think they can change the world are the ones who do.- Steve Jobs
6.A man can do a piece of work in 5 days, but with the help of his son, he can do it in 3 days. In what time can the son do it alone?
Option: B
son's 1 day's work = (1/3) - (1/5) = 2/15
i.e) the son alone can do the work in 15/2 days
7.A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With the help of C, they did the job in 4 days only. Then, C alone can do the job in:
Option: A
(A + B + C)'s 1 day's work = 1/4
A's 1 day's work = 1/16
B's 1 day's work = 1/12
C's 1 day's work = (1/4) - ((1/16) + (1/12)) = (1/4) - (7/48) = 5/48
so, C alone can do the work in 48/5 days
8.A takes twice as much time as B or thrice as much time to finish a piece of work.Working together, they can finish the work in 2 days. B can do the work alone in:
Option: B
suppose A, B and C take x, x/2 and x/3 hrs respectively to finish the work
then, (1/x) + (2/x) + (3/x) = 1/2
.i.e. 6/x = 1/2
x = 12 hrs, B = x/2 = 12/2 = 6 hrs
9.Harrison and Jade are working on an assignment. Harrison takes 6 hrs to type 32 pages on a computer, while Jade takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
Option: D
number of pages typed by Harrison in 1 hr = 32/6 = 16/3
number of pages typed by Jade in 1 hr = 40/5 = 8
number of pages typed by both in 1 hr = (16/3) + 8 = 40/3
Time taken by both to type 110 pages = (110) * (3/40)hrs = 33/4 hrs = 8 hrs 15 min
10.P can complete a work in 12 days working 8 hrs a day. Q can complete the same work in 8 days working 10 hrs a day. If both P and Q work together, working 8 hrs a day, in how many days can they complete the work?
Option: C
P can complete the work in(12 * 8)hrs = 96 hrs
Q can complete the work in (8 * 10)hrs = 80 hrs
P's 1 hrs work = 1/96
Q's 1 hrs work = 1/80
(P + Q)'s 1 hrs work = (1/96) + (1/80) = 11/480
so, both P and Q will finish the work in (480/11) hrs
number of days of 8 hrs each = (480/11) * (1/8) = 60/11 days
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