In a two-digit number, the digit at the unit's place is 1 less than twice the digit at the ten's place. If the digits at unit's and ten's place are interchanged, the difference between the new and the original number is less than the original number by 20. The original number is

Let two consecutive odd number be (A + 1) and (A + 3).
According to the question.
(A + 1) (A + 3) = 6723
? A² + 3A + A + 3 = 6723
? A² + 4A + 3 - 6723 = 0
? A² + 4A - 6720 = 0
? A² + 84A - 80A - 6720 = 0
? A(A + 84) - 80 (A + 84) = 0
? (A - 80) (A + 84) = 0
? A = 80, (A = ? - 84)
Hence, the greater number = 80 + 3 = 83

( A + B + C ) / 3 = 11111 ....(i)

Also, ( A+C ) / 2 = 11111 ....(ii)

From Eqs. (i) & (ii), we get
B = ? 11111 crore

? x = 2⁶⁴
? log x = log 2⁶⁴
? log x = 64 log 2
= 64 x .3010 = 19.264
? No.of digits = 19 + 1 = 20

36800 - 9999 - 3333 - 66 = 36800 - ( 9999 - 3333 - 66)
= 36800 - 13398
= 23402

Relative speed of the train
= (70 - 10)
= 60 km/hr
= (60 x 5/18)
= 50/3) m/sec.
? Time taken by the train to pass the man
= (100 x 3/50) = 6 sec.

7.2 kg = 7.2 x 1000000 gm = 7200000 gms
Required percentage = (18/7200000) x 100 % = 0.25%

In 19683, 19 lies between 2³ and 3³, so left digit is 2 and 683 ends with 3, so right digit is 7.
thus 27 is a cube root of 19683.

Area of the field =1215/135 = 9 hec
= 90000 m² [1 hec =10000 m²]
? Side of the field = ?90000 = 300 m
Perimeter of the field = 4 x 300 = 1200 m

Now, cost of putting a fence around field = (1200 x 75)/100 = ? 900