Question

the number of multiples of 3 or 5 but not 15 from 11 to 502 is?​

Answer 1

Answer:

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Answer 2

Question :- the number of multiples of 3 or 5 but not 15 from 11 to 502 is ?

Solution :-

Multiple of 3 :-

→ First number multiply by 3 from 11 to 502 = 12 = a

→ Last number = 501 = Tn

→ common difference = 3 = d (since multiple of 3).

→ Total number of terms = Let n

So, Using AP,

→ Tn = a + (n - 1)d

→ 501 = 12 + (n - 1)3

→ 501 = 12 + 3n - 3

→ 501 = 9 + 3n

→ 501 - 9 = 3n

→ 3n = 492

dividing both sides by 3,

→ n = 164.

Similarly,

Multiple of 5 :-

→ First number multiply by 5 from 11 to 502 = 15 = a

→ Last number = 500 = Tn

→ common difference = 5 = d (since multiple of 5).

→ Total number of terms = Let n

So, Using AP,

→ Tn = a + (n - 1)d

→ 500 = 15 + (n - 1)5

→ 500 = 15 + 5n - 5

→ 500 = 10 + 5n

→ 500 - 19 = 5n

→ 5n = 490

dividing both sides by 5,

→ n = 98.

Similarly,

Multiple of 15 :-

→ First number multiply by 15 from 11 to 502 = 15 = a

→ Last number = 495 = Tn

→ common difference = 15 = d (since multiple of 15).

→ Total number of terms = Let n

So, Using AP,

→ Tn = a + (n - 1)d

→ 495 = 15 + (n - 1)5

→ 495 = 15 + 15n - 15

→ 15n = 495

dividing both sides by 15,

→ n = 33.

Therefore,

→ Total numbers from 11 to 502 which are multiples of 3 or 5 but not 15 = Multiple of 3 + Multiple of 5 - multiple of 15 = 164 + 98 - 33 = 229 (Ans.)