(3x + 2) (2x - 5) = ax² + kx + n .

What is the value of a - n + k ?

Let the smaller number be 'm'

Then, from the given data, the larger number is '3m'

Given that m + 3m = 44

=> 4m = 44

m = 44/4 = 11

=> m = 11

=> 3m = 3 x 11 = 33

Hence, the two numbers are 11 and 33.

To find the largest 4 digit number exactly divisible by 88,

We should divide the largest possible 4 digit number by 88, and if we get any remainder than subtract it from that largest number.

The largest possible 4 digit number is 9999

Now,

88) 9999 (113
      88
  _______
      119
        88
  _______
        319
        264
  _______
          55
  _______

Therefore, the largest 4 digit number exactly divisible by 88 is given by

9999 - 55 = 9944.

Let the required number be 'p'.

From the given data,

p + 12 = 160 x 1/p

=> p + 12 = 160/p

=> p(p + 12) = 160

=> P^2 + 12p - 160 = 0

=> p^2 + 20p - 8p - 160 = 0

=> P(p + 20) - 8(p + 20) = 0

=> (p + 20)(p - 8) = 0

=> p = -20 or p = 8

As, given the number is a natural number, so it can't be negative.

Hence, the required number p = 8.

Let each literature text book cost be Rs. X

Then, cost of mathematics text book = Rs. (X + 2)

ATQ,

5X = 38 + 3(X + 2)

5X = 38 + 3X + 6

2X = 44

X = 22.

Therefore, cost of each literature text book = Rs. X = Rs. 22.

And that of masthematics = X + 2 = Rs. 24.

Let the larger number be p

Then, smaller number = 1/6 x p = p/6

Given difference between two numbers = 25

p - p/6 = 25

5p/6 = 25

5p = 150

p = 30

Then, p/6 = 30/6 = 5

Hence, larger number = 30 and smaller number = 5 which makes the difference = 25.

The difference between 4632 and 20000 is given by subtracting smaler number from the bigger number.

Here the bigger number is 20000

Smaller number is 4632

Now, subtracting 4632 from 20000

20000 - 4632 = 15368 and the resut is an even number.

Hence, The difference between 4632 and 20000 is 15368 and is an even number.

Let the number be 3p and 5p

ATQ,

8p = 2 x 48

p = 96/8

p = 12

The numbers are 36 and 60.

Hence, the product of the numbers = 36 x 60 = 2160.

Given 

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 + 1 + 1

Using BODMAS Rule,

As multiplication precedes addition, 1 x 0 = 0, 

Now, 10 + 0 + 1 + 1 = 10 + 2 = 12.

Hence, 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 x 0 + 1 + 1 = 12.