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 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.
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.
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
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