Question

Maths legends (100 points)

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

Answer 1

Answer:

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Answer 2

$\large \underline{\underline{\sf{\color{orange}{ANSWER:-}}}}$

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

$\large \underline{\underline{\sf{\color{orange}{TO\ FIND:-}}}}$

The sum of 2 digit number which are divisible by 3 and not divisible by 4.

$\large \underline{\underline{\sf{\color{orange}{SOLUTION:-}}}}$

◘ Case - 1

The two digit numbers which are divisible by 3 are  :-

12, 15, 18, ....., 96, 99

• Number of terms, n = 30
• Common difference, d = 3
• First term, a = 12

Then, the sum of the numbers divisible by 3 is  :

$\sf{S_n=\dfrac{n}{2}[2a+(n-1)d] }$

$\sf{\longrightarrow S_{30}=\dfrac{30}{2}[2(12)+(30-1)3] }$

$\sf{\longrightarrow S_{30}= 15(24+29\times3)}$

$\sf{\longrightarrow S_{30}= 15(24+87)}$

$\sf{\longrightarrow S_{30}= 15\times 111}$

$\sf{\longrightarrow S_{30}= 1665}$

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◘ Case - 2

Of the above numbers, which are divisible by 4 are

12, 24, 28, ....., 84, 96

• Number of terms, n = 8
• Common difference, d = 12
• First term, a = 12

Then, the sum of the numbers divisible by 4 is  :

$\sf{S_n=\dfrac{n}{2}[2a+(n-1)d] }$

$\sf{\longrightarrow S_{8}=\dfrac{8}{2}[2(12)+(8-1)12] }$

$\sf{\longrightarrow S_8=4(24+7\times12)}$

$\sf{\longrightarrow S_8=4(24+84)}$

$\sf{\longrightarrow S_8=4\times108}$

$\sf{\longrightarrow S_8=432}$

_____________________

◘ Now, the sum of 2 digit numbers which are divisible by 3 and not divisible by 4  = 1665 - 432

= 1233