Question

Deepak starts a work and work for 12 days and find he has completed 10% less work which he had to finish in order to complete the work in 24 days, so he ask Rahman to join him to finish the work on time. If Rahman work half day only for the remaining days. Find the efficiency of Rahman is what percent less than the efficiency of Deepak?​

Answer 1

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Deepak works for 12 days

so he should work (1/2)th part of the work.

but as, according to the question he completed 10% less than the required work in 12 days.

in 12days Deepak completed

$= ( \frac{1}{2} - 50\% \: of \frac{1}{2} )of \: the \: work \\ = \frac{1}{2} - \frac{10}{100} \times \frac{1}{2} \\ = \frac{50 - 5}{100} \\ = (\frac{45}{100} )th \: of \: the \: work$

so the remaining work is ...

$= (1 - \frac{45}{100} )th \: of \: the \: work \\ = ( \frac{55}{100} )th \: of \: the \: work$

so Deepak in rest of 12 days he will complete another(45/100)th part of the work.

that is in 24 days Deepak will complete

=[(45/100)+(45/100)]th of the work

=(90/100)th of the work.

So the remaining work=(1-90/100)=(10/100)th=(1/10)th part of the work will be completed by Ramesh in 12 days .

but Ramesh worked half days daily so show worked only (12/2)=6 days .

so in 6 days Ramesh worked=(1/10)th of the work

so in one day Ramesh worked=(1/60)th off the work.

So the efficiency of Ramesh is

$= \frac{1}{60} \times 100\% \\ = \frac{5}{3} \%$

Now ...

Deepak in 12 days worked( 45/100)th part of the work.

so in 1 day Deepak works=(45/1200)=(3/80)th of the work.

s0, efficiency of Deepak is

$= \frac{3}{80} \times 100\% \\ = \frac{15}{4} \%$

So the efficiency of Ramesh is less than by

=[(15/4)-(5/3)]%

=(25/12)% than the efficiency of Deepak

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