Answer: 1000

Explanation:
(1000)⁹ / 10²⁴   = (103)⁹ / 10²⁴ = (10)²⁷ / 10²⁴

Answer: 4

Explanation:
Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (10y + x) = 36
9(x - y) = 36
x - y = 4

Answer: 24

Explanation:
Let the ten's digit be x.
Then, unit's digit = x + 2.
Number = 10x + (x + 2) = 11x + 2.
Sum of digits = x + (x + 2) = 2x + 2.
(11x + 2)(2x + 2) = 144
22x2 + 26x - 140 = 0
11x2 + 13x - 70 = 0
(x - 2)(11x + 35) = 0
x = 2.
Hence, required number = 11x + 2 = 24.

Answer: 400

Explanation:
Let the numbers be x and y.
Then, xy = 9375 and x = 15.
y
xy = 9375
(x/y) 15
y2 = 625.
y = 25.
x = 15y = (15 x 25) = 375.
Sum of the numbers = x + y = 375 + 25 = 400.

Answer: 253

Explanation:
Let the middle digit be x.
Then, 2x = 10 or x = 5. So, the number is either 253 or 352.
Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.
Hence, required number = 253.

Answer: 1

Explanation:
For x=2, the numbers are: 2, 4, 6 … (only first number is a prime number)
For x=3, the numbers are: 3, 5, 7 … (all numbers are prime numbers)
For x=5, the numbers are 5, 7, 9 … (first two numbers are prime numbers)
Hence for all other possibilities of x as a prime number, x, x+2 and x+4 all are not prime numbers.
Therefore there is only one possibility of x.

Answer: 72

Explanation:
Let the number be x.
3/4x = 2/3x + 8
Multiply by 12
9x = 8x + 72
x = 72

Answer: 12

Explanation:
As the division is by 2, 3, 7 together, the numbers are to be divisible by: 2*3*7 = 42
The limits are 100 and 600
The first number divisible is 42*3 = 126
To find out the last number divisible by 42 within 600:
600/42 = 14.28
Hence, 42*14 = 588 is the last number divisible by 42 within 600
Hence, total numbers divisible by 2, 3, 7 together are (14 – 2) = 12

Answer: 1

Explanation:
The number is 1

Answer: 8, 2

Explanation:
As 88 is an even number, option (c) and (d) are eliminated. Substituting the values of (a) and (b) and solving the answer is (a)