Work rate of A = $$\frac{{100}}{9}$$ = 11.11% work per day
Work rate of B = $$\frac{{100}}{{15}}$$ = 6.66% work per day

They toger can do (A + B) = 11.11 + 6.66 ≈ 18% work per day
They are working in alternate day, so we take 2 days = 1 unit of day
Therefore, in one unit of day y can complete 18% of work
(A + B) can complete 90% of work in 5 units of days. i.e. (5 × 18)
And rest 10% work will be completed by A in Next day
So, total number of day,
= 5 Unit of days + 1 day of A
= 2 × 5 + 1 = 11 days

$$\eqalign{ & 20\% = \frac{1}{5}\left[ {{\text{efficiency}} \propto \frac{1}{{{\text{days}}}}} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{A }}:{\text{ B}} \cr & {\text{Efficiency}}\,\,\,\,\,\,4{\text{ }}:{\text{ }}5 \cr & {\text{Days}}\,\,\,\,\,\,\,\,\,\,\mathop {\mathop 5\limits_{{\text{ }} \downarrow \times 2} }\limits_{10\,{\text{days}}} :\mathop {\mathop 4\limits_{{\text{ }} \downarrow \times 2} }\limits_{{\bf{8}}\,{\bf{days}}} \cr} $$

P complete $$\frac{1}{4}$$ th of work in 10 days
So, P will complete whole work in 40 days.
Q completes $$\left( {40\% = \frac{2}{5}{\text{th}}} \right)$$   work in 40 days
Q will complete whole work in = $$\frac{{40 \times 5}}{2}$$ = 100 days
R completes $$\frac{1}{3}$$ work in 13 days
R will complete whole work in = 39 days
Work will be finished firstly by man who will take less days to complete it,
So, R will complete it first.

Water filled by (boy + girl) in one minute,
$$\eqalign{ & \frac{4}{3} + \frac{3}{4} = \frac{{16 + 9}}{{12}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{25}}{{12}}\,{\text{liter}} \cr} $$
Hence, time taken to fill 100 liter,
$${\text{ = 100}} \times \frac{{12}}{{25}} = 48\,{\text{minutes}}$$

Efficiency of Raj = $$\frac{{100}}{{20}}$$ = 5%
Work completed by Raj = 25%
Rest work = 75%
Efficiency of Abhijit = $$\frac{{75}}{{10}}$$ = 7.5%
Combined efficiency = 5 + 7.5 = 12.5%
They will complete whole work by working toger in,
= $$\frac{{100}}{{12.5}}$$ = 8 days

3 men or 4 women can plough field in 43 days
3 men = 4 women
1 man = $$\frac{4}{3}$$ women
7 man = $$\frac{{28}}{3}$$ women
7 men and 5 women = $$5 + \frac{{28}}{3}$$  = $$\frac{{43}}{3}$$ women
4 women can plough field in 43 days
So,
1 women can plough in = 43 × 4 days
Hence,
$$\frac{{43}}{3}$$ women can plough = $$\frac{{43 \times 4 \times 3}}{{43}}$$   = 12 days

Let capacity of tank = q litres
According to question,
Quantity of water emptied by leak in 1 hour = $$\frac{\text{q}}{10}$$ litres
Qunatity of water filled by tap in 1 hour = 240 litres
According to question,
$$\eqalign{ & \Rightarrow \frac{{\text{q}}}{{10}} - \frac{{\text{q}}}{{15}} = 240 \cr & \Rightarrow \frac{{3{\text{q}} - 2{\text{q}}}}{{30}} = 240 \cr & \Rightarrow \frac{9}{{30}} = 240 \cr & \Rightarrow {\text{q}} = 240 \times 30 \cr & \Rightarrow {\text{q}} = 7200\,{\text{litres}} \cr} $$

Total efficiency of two persons = 50% [As y complete work in 2 days. ]
First Person completes work = $$\frac{1}{3}$$ = 33.33% [In 2 days]
Rest work will be completed by Second man = $$\frac{2}{3}$$ = 66.66% [In 2 days]
So, efficiency of second person is greater.
Efficiency of second person = $$\frac{{66.66}}{2}$$  = 33.33% per day
Then, Second person will complete whole work in,
= $$\frac{{100}}{{33.33}}$$  = 3 days.

P can fill cistern in 12 minutes
P fills cistern in 1 minute = $$\frac{1}{{12}}$$
Q can fill cistern in 15 minutes
Q fills cistern in 1 minute = $$\frac{1}{{15}}$$ part
P and Q toger can fill cistern in 1 minute,
$$ = \frac{1}{{12}} + \frac{1}{{15}} \Rightarrow \frac{9}{{60}}$$    part
So, y can toger fill cistern in 3 minute,
$$ = 3 \times \frac{9}{{60}} \Rightarrow \frac{9}{{20}}$$    part
Rest Cistern = $$1 - \frac{9}{{20}}$$  = $$\frac{{11}}{{20}}$$  part
$$\frac{{11}}{{20}}$$ part cistern must be filled by Q in
$$\frac{{\frac{{11}}{{20}}}}{{\frac{1}{{15}}}} = 8\frac{1}{4}$$   minutes

Alternatively,
Pipe P can fill cistern in one minute = $$\frac{{100}}{{12}}$$ = 8.33%
Pipe Q can fill cistern in one minute = $$\frac{{100}}{{15}}$$ = 6.66%
(P + Q) toger can fill cistern in one minute = 15%;
In 3 minutes cistern is filled = 45%
P become off, n rest of cistern will be filled by Pipe Q in = $$\frac{{55}}{{6.66}}$$ = $$8\frac{1}{4}$$ minutes.