. Two friends Kallis
work separately they
work of levelling,
alternately for one
Kallis and Clerk take up the work of levelling the field. If they
stely they take 8 hours and 12 hours respectively to finish the
muelling the ground. They decide to finish the work doing it
for one hour each and so on till it is finished. If they start work
+ 7 A.M., when will they finish the work?
(B) 4:30 P.M.
(D) 5:30 P.M.
(A) 4 P.M.
(C) 5 P.M.
(E) None of these
every two hours they complete 1/8 + 1/12 = 5/24 of the job
So, after 8 hours, they have done 20/24 of the job, leaving 1/6 still to do
Since neither can do 1/6 of the job in an hour,
It will take another 1+ hours to finish, so it will be between 4 and 5 pm.
Total work =1
Kallis works in 1 hour = 1/8
Clerk works in 1 hour = 1/12
Work finished in 2 hours = 1/8+ 1/12= 5/24
Works finished in 8 hours = 5/24 × 4 = 20/24
Now Kallis work 9th hour = 20/24 + 1/8 = 23/24
Remaining work= 20/24 - 23/24 = 1/24
Now clerk works half hour = 1/12 × 1/2 = 1/24
So total time = 9 and half hour
Now time = 7A.M + 9:30 = 4:30 PM
1/8 + 1/12 = 3/24 + 2/24 = 5/24
they do that much every 2 hours. So, in 8 hours they do 4 times that much: 20/24
The 4/24 left = 1/6
Looks like you need to work on your fractions some.
if my teacher ask me how 20/24 came ??
How 1/6 came??
How will I explain???
E) None of these. They will never finish the work because Kallis and Clerk will keep taking turns to work on the field indefinitely. They should consider hiring someone else to help them finish the job.
To find out when Kallis and Clerk will finish the work, we need to determine the total amount of time it takes for both of them to complete the levelling.
We are given that Kallis takes 8 hours and Clerk takes 12 hours to finish the levelling on their own.
To find the time it takes for both Kallis and Clerk to finish the work when they work together, we can use the formula:
1/T total = 1/T1 + 1/T2
Where T total is the combined time, T1 is the time taken by Kallis alone, and T2 is the time taken by Clerk alone.
Substituting the given values, we have:
1/T total = 1/8 + 1/12
Next, we need to find the least common multiple (LCM) of 8 and 12, which is 24.
Multiplying both sides of the equation by 24, we get:
24/T total = 3 + 2
24/T total = 5
Now, we can find T total by taking the reciprocal of both sides:
T total = 24/5 = 4.8 hours
Since they start working at 7 A.M., we can add 4.8 hours to the starting time to find when they will finish the work.
7 A.M. + 4.8 hours = 11:48 A.M.
Therefore, the work will be finished at 11:48 A.M.
None of the answer choices provided match the calculated time, so the correct answer would be "None of these" (E).