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Santosh kumar Maharana

· started a discussion

· 1 Months ago

Difficult solution (Question: 99433.0 )

Please provide so easy solution of this question so that I can understand. The solution which is provided seems more difficult & not easy to understand.

Question:

Two workers undertake to do a job. The second worker started working 2 hours after the first. Five hours after the second worker has begun working there is still 9/20 of the work to be done. When the assignment is completed after another 5 hours, it turns out that first worker has done 60% of the work, while second worker has done rest of the work. How many hours would take each one to do the whole job individually?

Options:
A) 10 hours and 12 hours   
B) 15 hours and 10 hours
C) 20 hours and 25 hours 
D) 18 hours and 20 hours
E) None of these
Solution:
Go through option. Consider choice (c). 

Efficiency of first worker = 5% 

Efficiency of second worker = 4% 

∴ In 7 hours first worker completed 35% work 

In 5 hours second worker completed 20% work 

Thus, work completed = 55% 

Remaining work = 45%

Hence, one condition is satisfied. 

Again, they will take 5 more hours to complete 45% work 

\(\big[ \cfrac{45}{4+5}=5\big]\)

Thus, first person completes 7 × 5 + 5 × 5 = 60% work and second person completes 5 × 4 + 5 ×4 = 40% work 

Hence, second condition is also satisfied. Hence, correct option is (c).

ABHII

· commented

· 1 Months ago

Hi Santosh,
Go through the explanation given below:

As the question is asking the individual time of both to complete the work. So the given choice are the no. of days taken by A and B to complete the work individually.(let A is the first person and B is the second)
Consider choice (c)

Given that the A takes 20 hours to complete the work so his one hour work will be 1/20 or we can say Efficiency of A = 5%
Similarly B takes 25 hours to complete the work so his one hour work will be 1/20 or we can say Efficiency of B = 4%
∴ In 7 hours A completed 5%*7=35% work
In 5 hours B completed 4%*5=20% work
(why taking 7 hours for A, 5 hours for B- it has mentioned in the question that after B has worked for 5 hours it has found 9/20 work is still remained and A was working from 2 hour before B that's why taken 7 hours for him)

Thus, work completed = 55%
Remaining work = 45%
As question has also mentioned the same(9/20 work remaining it means 11/20 has been finished till the time)
Hence, one condition is satisfied.

Another condition is given that A has done 60% of the whole work and B has done remaining 40%.
As per their efficiencies if both of them working together so they can complete the 9% work per hour so it will take 5 more hours from this point to complete the whole work. as explained further.[
454+5=5]

Now we can count the total part as we know that A has worked for 12 hour in all and B has worked 10 hours.
by the calculation we can find that A did 5%*12=60% and B did 4%*10=40% which is the second condition
here in the solution the same thin has been explained in a different way that A has firs worked for 7 hours and then for 5 more, similarly B has worked initially 5 hours and the 5 hour more.
Thus, first person completes 7 × 5 + 5 × 5 = 60% work and second person completes 5 × 4 + 5 ×4 = 40% work
Hence, second condition is also satisfied. Hence, correct option is (c).
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