Two men A and B travel from point P to Q, a distance of 84 km at 12 km/h and 16 km/h, respectively. B reaches Q and returns immediately and meet A at R. Find the distance form P to R.

(A + B +)'s 2 h work = 1/8 + 1/12 = 5/24
(A + B)'s 8 h work = (5 x 8)/(24 x 2) = 5/6
Work done by A in 9th h = 1/8
Total work done upto 9th h = 5/6 + 1/8 = 23/24
Remaining wok = 1/24
B's 1 h work = 1/12
B can do 1/24 of the work = (1/24) x 12 = 1/2 h
So, both can finish the job in 9¹/₂ h.

Let Rohit, Harsh and Sanjeev can type x, y and z pages respectively in 1 h.
Therefore, they together can type 4(x + y + z) pages in 4 h
? 4(x + y + z) = 216
? x + y + z = 54 .....(i)
Also, z - y = y - x
i.e., 2y = x + z ......(ii)

From Eqs. (i) and (ii), we get
3y = 54
? y = 18

From Eq. (ii), x + z = 36 ....(iv)
From Eqs. (iii) and (iv),
we get x = 15 and z = 21

(A + B)'s one day work = 1/12
(B + C)'s one day work = 1/16
Now, from the question,
A's 5 days work + B's 7 days work + C's 13 days work = 1
? A's 5 days work + B's 5 days work + B's 2 days work + C's 2 days work + C's 11 days work = 1
(A + B)'s 5 days work + (B + C)'s 2 days work + C's 11 days work = 1
? 5/12 + 2/16 + C's 11 days work = 1
? C's 11 days work = 1 - (5/12 + 2/16) = 11/24
? C's 1 day work = (11/24) x 11 = 1/24
Hence, C can do this work in 24 days.

Fraction of work complete by (A and B) + Fraction of work complete by (B and C) + Fraction of work completed by C = 1
As B did the work for 8 days we can say B did the work for 3 days with A and B did the work for 5 days with C. So, A and B together did the work for 3 days, B and C together did the work for 5 days, C alone did the work for 5 days.
? 3/12 + 5/15 + 5/x = 1 or 5/x = 5/12
i.e., x = 12 or C alone can complete the work in 12 days

Since, 50 men can do a job in 50 days.
So, work done by 1 man in a day = 1/(50 x 50)

Also, 80 women can do the job in 50 days.
So, work done by 1 women in 1 day = 1/(50 x 80)

Now, work done by 40 men and 48 women in first 10 days
= (40 x 10)/(50 x 50) + (48 x 10)/(50 x 80)
= 4/25 + 3/25 = 7/25

Now, 5 men and 8 women are removed after 10 days,
So work done by 35 men and 40 women in 10 days = (35 x 10)/(50 x 50) + (40 x 10)/(50 x 80)
= 7/50 + 1/10 = (7 + 5)/50
= 6/25

Again, 5 men and 8 women are removed after 10 days,
So work done by 30 men and 32 women in 10 days = (30 x 10)/(50 x 50) + (32 x 10)/(50 x 80) = 5/25

Now, after every 10 days as the number of men and
women decrease, work done also decreased by 1/25th past.
So, work done after every 10 days upto 50 days = 7/25 + 6/25 + 5/25 + 4/25 + 3/25
= 25/25 = 1

So, it will take 50 days for them to complete the work.

Time taken by one tap to fill half of the tank = 3 hrs.

Part filled by the taps in 1 hour = 4 x 1/6 = 2/3

Remaining part = 1 - 1/2 = 1/2

2/3 : 1/2 :: 1 : p

p = 1/2 x 1 x 3/2 = 3/4 hrs. i.e., 45 min

So, total time taken = 3 hrs 45 min.

Let pipe A takes p min to fill

Then,

pipe B takes 3p min to fill

=> 3p - p = 32

=> p = 16 min => 3p = 48 min

Required, both pipes to fill = (48 x 16)/(48 + 16) min = 12 min.

The time taken by the leak to empty the tank =  1 8 - 1 10 = 5 - 4 40 = 1 40

Therefore, the leak empties the tank in 40 hours.

Given that the waste tap can empty the filled tank in 32 min.

Now, the rate at which the waste tap can empty the tank = (40 + 60)8/32 = 100/4 = 25 lit/min.

A's 5 day work = 50%
B's 5 day work = 33.33%
C's 2 day work = 16.66% [100 - (50 + 33.33)]
Ratio of contribution of work of A , B and C = 50 : 33.33 : 16.66 = 3 : 2 : 1
A's total share = Rs. 1500
B's total share = Rs. 1000
C's total share = Rs. 500

A's one day's earning = Rs. 300
B's one day's earning = Rs. 200
and C's one day's earning = Rs. 250