1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, and 2000 are 20 positive factors of 2000.

Hence, option D is the correct answer.

Let the length of the train is x and that of the platform is 2x.

Here, Speed of the train = 144 km/hr

= 144×5/18 = 8×5 = 40 m/s

And, Time = 30 sec

Now, according to the question,

⇒ = 30; (distance/speed = time)

⇒ 3x = 1200

⇒ x = 1200/3 = 400

∴ Length of the platform

= 2 × 400 = 800 metres

Since 88 = 8 × 11

The number must be divisible by 8 and 11 individually

First, rule of divisibility by 8:

Last three digits of the number must be divisible by 8.

Therefore, the last three digits (10x) of the number will be 104. (no other digit will make it divisible by 8)

Therefore, x = 4.

Now, rule of divisibility by 11:

Difference between sum of digits at odd place and sum of digits at even place must be divisible by 11.

Therefore,

(2 + 6 + 1 + 4) – (y + 8 + 0) = 11n, where n is any integer

⇒ 13 – (y + 8) = 11n

⇒ –y + 5 = 11n

⇒ –y + 5 = 0 (n = 0, because n = 1 will make ‘y’ negative and -1 will make ‘y’ a double digit number)

Therefore, y = 5.

Now, (x) × (y) = 4 × 5 = 20

Given:

Profit at Selling Price of Rs. 6250 = Loss at Selling Price of Rs. 3750

⇒ 6250 – Cost Price = Cost Price – 3750

⇒ CP + CP = 6250 + 3750

⇒ 2CP = 10000

⇒ CP = 10000/2 = 5000

Therefore, cost price of the article is Rs. 5000.

Let sale on 5^th day = ₹ x

Average sale of all 5 days = ₹3,500

⇒ (14000 + x)/5 = 3500

⇒ 14000 + x = 17500

⇒ x = 17500 – 14000

⇒ x = 3500

Hence, sale on 5^th day = ₹ 3500

If pipe A, B and C are opened together, they took 80 minutes to empty  of the tank.

We know that 80 minutes =

So, tank emptied by pipe A and B in  of the tank

Here, the negative sign only shows that tank is emptied by Pipe A and

B.

Tank emptied by pipe A, B and C in  of the tank.

Tank filled by pipe C in 80 minutes = of the tank

Tank filled by pipe C in 60 minutes =  of the tank

Hence, Pipe C alone can fill the tank in 48 hours.

In class IX, the average of marks in science for six students was 48.

Sum of marks in science for six students = 48×6 = 288

After result declared, it was found in case of one student, the marks 45 were misread as 54.

So, Correct sum of marks in science for six students = 288 – 54 + 45 = 279

Correct average = 279/6 = 46.50

Let the income of the man be 100P.

Expenditure of man = 75P

Savings of man = 100P – 75P = 25P

Now, income increases by 28%, then

New income = 128P

New expenditure = (100 + 20)% of old expenditure = 120/100 * 75P = 90P

New savings = new income – new expenditure = 128P – 90P = 38P

Percentage increase in savings = (38P – 25P)/25P × 100= 52%

 Let

Where, P = Principal borrowed

⇒ x = Annual instalments

⇒ R = Rate of interest

⇒

⇒  = Rs. 11340

Hence, Principal borrowed = Rs. 11340

Compound interest = Total instalment amount – Principal =