In the year 2011, Shantanu gets a total of 3832.5 Rupee as his pocket allowence. Find his pocket allowence per day.

Let four consecutive even numbers are x, x+2, x+4, x+6.
According to the question
? x + x+2 + x+4 + x+6 = 284
? 4x + 12 = 284
? 4x = 272
? x = 272 / 4 = 68

Let the two consecutive odd number be (x + 1) and (x + 3).
According to question (x + 1) (x + 3) = 6723
? x² + 3x + x + 3 = 6723
? x² + 4x + 3 = 6723
? x² + 4x - 6720 = 0
? x² + 84x - 80x - 6720 = 0
? ( x - 80 )( x + 84 )= 0
? x = 80, (x ? -84)
Hence, the greater number = 80 + 3 = 83

Prime number less than 40 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37
? The number of all prime numbers less than 40 = 12.

It is clear from expression is that remainder is 18

Let number be the x.
According to the equation , x - ^x?₇ = 180
? ^6x?₇ = 180
? x = 210

prime numbers between 0 and 50 are 2 3 5 7 11 13 17 19 23 29 31 37 41 43 and 47
? required number of prime number is 15

5,15,25,35,40,50,55,65,75,85,95
So there are total 11 such type of numbers.

Let be the ten's digit be x and unit's digit be y.
So the two digit number = 10x + y ( where x > y )
According to question
x + y = 14 ....(i)
x - y = 2 ....(ii)

Solving Eqs. (i) and (ii), we get
x = 8 and y = 6
? Required product = 8 x 6 = 48

There can be infinite number of rational numbers between 1 and 1000.