Question

Find the sum of 2 digit number which are divisible by 3 and not divisible by 4​

Answer 1

Arithmetic Progression

• The two digit numbers which are divisible by 3 are
• 12, 15, 18, ....., 96, 99
• Number of terms = 30
• Common difference = 3
• So, the sum of the numbers divisible by 3 is
• = 30/2 * [12 + 99]
• = 15 * 111
• = 1665

• Of the above numbers, which are divisible by 4 are
• 12, 24, ....., 84, 96
• Number of terms = 8
• Common difference = 12
• Their sum is
• = 12 + 24 + 36 + 60 + 72 + 84 + 96
• = 8/2 * [12 + 96]
• = 4 * 108
• = 432

• Hence the sum of 2 digit numbers which are divisible by 3 and not divisible by 4 is
• = sum of the 2 digit numbers divisible by 3 - sum of the 2 digit numbers divisible by 4
• = 1665 - 432
• = 1233

Answer: The sum of 2 digit numbers which are divisible by 3 and not divisible by 4 is 1233.

Answer 2

question➡Find the sum of 2 digit number which are divisible by 3 and not divisible by 4Find the sum of 2 digit number which are divisible by 3 and not divisible by

4.

☣☣answer➡1233

_________________

solutiion➡➡➡

sum of all-2digit number divisible by 3 be sn

sn=a+a+d.............a+(n-1)d

here➡a=12,d=3

1st number is 12 and last numbe is 99

we know,

An=a+(n-1)d

==>99=12+(n-1)3

==>99-12=3n-3

==>87+3=3n

$= = > n = \frac{90}{3} \\ \\ \boxed{ = = > n = 30}$

Hence,

$\bf\ sn = 30 \times 12 + \frac{29 \times 30 \times 3}{2} \\ \\ \bf\ \implies: 360 + 29 \times 15 \times 3 \\ \\ \bf\boxed{ \implies:1665 }$

The number which are divisible by 4 and 3 ➡

4×3,4×2×3,...................4×8×3

Let,

sn1 denot the sum of the numbers which are divisible by 3 and 4

☣sn1=4×3+4×2×3+..............+4×8×3

==>4×3{1+2+3+4+5+6+7+8} [common 4×3]

==>12×36

==>432

$\bf\pink{ \underline{the \: sum \: of \: numbers \: divisible \: by \: 3}} \\ \bf\red{ \underline{but \: not \: divisible \: by \: 4 \: is \mapsto}} \\ \\ \bf\purple{ \boxed{ \bigstar \: sn \: - sn1 = 1665 - 432 = 1233}}$