Question

i) How many two digit numbers are divisible by 3?​

Answer 1

$\sf\huge \pink{ Solution :}$

$\sf 12, 15, 18,. \: . \: .19$

$\sf a = 12 \: \: n = 3 \: \: An = 99$

$\sf An = a + ( n - 11n )$

$\sf 99 = 12 + ( n - 11³ )$

$\sf 99 = 12 + 3n - 3$

$\sf 99 = 12 - 3 + 3n$

$\sf 99 = 9 + 3n$

$\sf 99 - 9 = 3n$

$\sf 90 = 3n$

$\sf n = \frac{90}{3} = 30 = n = 30$

$\sf \pink{ There \: are \:  30 \: two \:  digit \: numbers \: are \: divisible \: by \: 3.}$