Let's solve this step by step.

Step 1: Write compound interest formula

Here,

Step 2: Simplify

So,

Step 3: Divide

✅ Answer: 22000

Given:

Pipe P + Pipe Q = 60/7 minutes

Pipe P + Pipe Q - Pipe R = 300/23 minutes

Pipe P : Pipe Q = 3 : 4

Formula:

If time taken by pipe A to fill tank is ‘a’ minutes and by pipe B is ‘b’ minutes then total time taken to fill the tank t ⇒ (1/t) = (1/a) + (1/b)

Calculation:

Let, time taken by pipe P be X

⇒ Time taken by pipe Q = 4 × X/ 3

⇒ 7/ 60 = (1/ X) + (3/(4X))

⇒ 7/ 60 = (4 + 3)/4X

⇒ 7/ 60 = 7/4X

⇒ 60 = 4X

⇒ X = 15

⇒ Time taken by pipe Q = 20 (∵ 4 × 15/3 = 20)

Let, time taken by pipe R be Y

⇒ 23/ 300 = (7/ 60) - (1/Y)

⇒ 1/ Y = (7/ 60) - (23/300)

⇒ 1/ Y = (35 – 23)/300

⇒ Y = 25 (∵ 300/12 = 25)

Now finding time taken by Q and R to fill the tank

⇒ 1/ t = (1/ 20) - (1/25)

⇒ 1/ t = (25 - 20)/500

⇒ 1/ t = 1/100

⇒ t = 100/1 minutes

∴ it takes 100 minutes to fill the tank

Time taken by two pipe to fill a tank is 60/ 7 = 8.57 min (approx.)

Confusion Points

Time taken by three pipe to fill a tank is 300/ 23 = 13 min (approx.)

As three pipe together takes more time than two pipes.

That means the one pipe drain pipe taking water out of tank.

Hence, R time is been subtracted.

Given:

Speed of train 1 = 46 km/h

Speed of train 2 = 36 km/h

Time to overtake = 36 seconds

Concept:

Relative speed = Speed of train 1 - Speed of train 2

Distance = Speed × Time

Length of the train = Distance/2 (since two trains of equal length are involved)

Solution:

⇒ Relative speed = 46 km/h - 36 km/h = 10 km/h = 10 × 1000/3600 m/s (converted from km/h to m/s)

⇒ Distance travelled during the overtake = Relative speed × Time = 10 × 1000/3600 m/s × 36 s = 100 m

⇒ Length of each train = Distance/2 = 100/2 = 50 m

Hence, the length of each train is 50 meters.

Let's solve this step by step.

Step 2: Form equations

From first condition:

From second condition:

Step 5: Required time

We need time for 55 km downstream + 14 km upstream:

✅ Answer: 7 hours

Let's solve this carefully step by step.

Step 1: Work done by 8 workers

✅ Answer: 15 days

We need to solve this step by step.

Step 1: Condition for numbers to be in proportion

✅ Answer: 2

Let's work it out step by step.

First man schedule (starting 11:00 a.m.):

• Runs 11:00–13:00 at 10 km/h → covers 20 km.

• Rests 13:00–14:00 (position stays 20 km).

• Repeats: runs 14:00–16:00 (another 20 km), rests 16:00–17:00, etc.

So at 2:00 p.m. (14:00), when the second man starts, the first man is at 20 km and is starting a 2-hour run.

Let t = hours after 2:00 p.m.