There can be infinite number of rational numbers between 1 and 1000.
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
5,15,25,35,40,50,55,65,75,85,95
So there are total 11 such type of numbers.
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
Allowance per day = total allowance / number of days in year
= 3832.5 / 365
= 10.5 Rupees
Let 5 consecutive even number be A = x, B = x+2, C = x+4, D = x + 6 and E = x + 8.
According to question
x + x +2 + x + 4 + x + 6 + x + 8 = 130
? 5x + 20 = 130
? x = 22
? A = 22, E = 22 + 8 = 30.
? Multiplication of A and E = 22 x 30
= 660
Let smallest number = x.
Then, x + x + 1 + x + 2 + x + 3 + x + 4 = 170
? 5x + 10 = 170
? x = 160 / 5
? x = 32
? product of smallest and largest number = 32 x 36
= 1152
Let the two consecutive odd numbers be 2x+1 and 2x + 3 .
? Difference = ( 2x + 3 )2 - ( 2x + 1 )2
= ( 2x + 3 + 2x + 1 )( 2x + 3 - 2x - 1 )
=( 4x + 4 ) x 2
= 8 (x + 1)
whis is exactly divisible by 8.
9856 x 156 + 9856 x 844 = 9856 x (156 + 844)
= 9856 x 1000
= 9856000
6674 x 625 = 6674 x (5)4
= 6674 x (104/24
= 66740000/16 = 4171250
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