Combined formula for Time and Work
Another important concept that is used in time work problems is the combined efficiency of
two or more persons. In questions on time and work, the rates at which certain persons or
machines work alone are usually given, and it is necessary to compute the rate at which they
work together (or vice versa).
Let us say, for example, it takes 3 & 6 hours for Bahubali and Kattappa, respectively, to
break a dam working alone. So, in 1 hour Bahubali would have broken one-third or 1/3rd or
33% of the dam and Kattappa would have broken one-sixth or 1/6th or 16.67% of the dam.
In 2 hours, Bahubali would have destroyed 1/3*2 or 33% *2 = 66.66% of the dam and
kattappa would have destroyed 1/6th *2= 1/3= 33.33% of the dam. So if Both Bahubali and
Kattappa work together, they would have destroyed 66.66+ 33.33 (2/3+1/3) or 100% of the
dam in 2 hours. Therefore, if both worked together for 1 hour, they would have destroyed 1/3
+ 1/6= ½ or half of the dam. Thus in 2 hours, the dam is destroyed.
Generalizing, we conclude that in 1 hour, Bahubali does 1/r of the job, Kattappa does 1/s of
the job, and Bahubali & Kattappa together do 1/h of the job or that together they can finish
the job in ‘h’ hours where the formula for work comes out as 1/r + 1/s = 1/h.
Try to solve the following time and work questions using time and work formula:
Q.1.In the beginning, Ram works at a rate such that he can finish a piece of work in
24 hrs, but he only works at this rate for 16 hrs. After that, he works at a rate such
that he can do the whole work in 18 hrs. If Ram is to finish this work at a stretch, how
many hours will he take to finish this work?
a) 12 hrs
b) 18 hrs
c) 11½ hrs
d) 15 hrs
e) 22 hrs
Explanation:Ram’s 16 hr work = 16/24 = 2/3. Remaining work = 1 – 2/3 = 1/3.
ReplyDeleteUsing work and time formula: This will be completed in 1/3 × 18 i.e. 6 hrs.
So, total time taken to complete work = 16 + 6= 22 hrs.
Given : Ram works at a rate such he will end a chunk of labor in twenty-four hours, however, he solely works at this rate for sixteen hrs.
ReplyDeleteAfter that, he's employed at a rate such he will do the complete add eighteen hrs.
According to the question,
Ram’s sixteen time unit work = 16/24 = 2/3.
Remaining work = one – 2/3 = 1/3.
Using work and time formula:
This will be completed in 1/3 × eighteen i.e. 6 hrs.
So, the total time is taken to finish work = 16 + 6
= 22 hours.
e) 22 hours
ReplyDeleteWork done in beginning = 16/24 = 2/3
Total work =1
Remaining work= 1 - 2/3 = 1/3
Applying work time formula= 1/3 *18 = 6 hours
Total time to complete work = 16+6 = 22 hours
correct
DeleteWork done in beginning =16/24 = 2/3
ReplyDeleteTotal work = 1
Remaining work= 1-2/3 = 3-2/3 =1/3
Using time formula 1/3*18 = 6
Total time needed= 16+6= 22
E) 22
Ans- e) 22hrs
ReplyDeleteTotal Work- 1
Work done in the beginning- 16/24= 2/3
Remaining Work- 1-2/3= 3-2/3=1/3
1/3*18 =6 hours ----------( Work time formula)
Therefore total time needed to complete work => 16+6 = 22 hours
-Rishika Kushwaha
DeleteGood Rishika !
ReplyDeleteAns- e) 22hrs
ReplyDeleteWork done in the beginning→ 16/24= 2/3
Total Work→ 1
Remaining Work →1-2/3
→ 3-2/3
→ 1/3
By using the work time formula, the work will be completed in:
1/3*18 =6 hours
Therefore total time needed to complete work→16+6 = 22 hours
Sanjam Bedi
10-B
Work done by Ram in the beginning = 16/24 = 2/3
ReplyDeleteTotal Work = 1
Remaining Work = 1- 2/3 = 1/3
By using the time and work formula , the time taken to complete remaining work= 1/3 * 18 hr = 6hr
Therefore, Total time taken to complete work = 16 hr + 6 hr = 22 hr.
Hence, option (e) 22 hrs is the answer.
-By Somil Kashyap
Well done children.
ReplyDelete