Question

A group of 30 people can complete a job by working for 10 h
a day in 15 days. The group starts the work. But at the end of
every day, starting from the first day, one person leaves the
group and the remaining people work for 20 min less on the
next day.

Q.49 On which day will the work be completed?
(a) 28h
(b) 29th
(C) 30th
(d) None of these
Q.50 What part of the work, approximately remains to be
done at the end of 15 days?
(a) 0.51 (b) 0,61
(c) 0.49
(d) 0.39​

Answer 1

Answer:

Step-by-step explanation:

c)30th

Answer 2

Answer:

For Q49 - d - None of these

For Q50 - d - 0.39

Step-by-step explanation:

Q 49.

So let's suppose the efficiency of 1 person = p and total work = w units.

The formula for Work and Efficiency is:

Efficiency of 1 person = (Total Work)/(Total Time)

So, it is given that,

30*p = w/(10*15)

p = w/4500

Now, variation of the same formula used above,

Efficiency*(Number of persons * Time) = Total Work

(w/4500) * (30*10 + 29*(10-1/3) + 28*(10-2/3) + ... ) = w

Multiplying both sides by 3,

3 * ( 30*10 + 29*(10-1/3) + 28*(10-2/3) + ... ) = 3 * 4500

30^2 + 29^2 + .... = 13500

Now, finding number of terms at LHS will give us number of days taken.

Now, lets take the highest possible value i.e. 30.

30^2 + 29^2 + .... + 1^2 = 13500 -- ( Eq. 1 )

Now, we have a standard formula to solve LHS (you can google it if you don't know) and solving it gives:

9455 = 13500, which is still lesser than RHS.

So, answer is "Not possible" because number of persons will become negative for more than 30 days.

Q 50.

Now see Eq. 1 in above question but here they worked for 15 days so now the equation becomes:

30^2 + 29^2 + .... + 16^2 = 13500x, where x is the fraction of work done yet.

( 30^2 + 29^2 + .... + 1^2 ) - ( 15^2 + 14^2 + .... + 1^2 ) = 13500x

9455 - 1240 = 13500x

x = 8215/13500 = 0.61

So work remaining = 1 - 0.61 = 0.39.