Question

How many nos are between 11 and 90 which are divisible by 7?

Answer 1

there are eleven nos. between 11 and 90 which are divisible by 7.

Answer 2

(1) Finding the least multiple of 7 after 11...

 

For finding this, divide 11 by 7, add 1 to the quotient, and then multiply it by 7.

  ⇒ Divide 11 by 7. We get quotient 1.

  ⇒ Add 1 to the quotient. We get 2.

  ⇒ Multiply this 2 by 7. We get 14.

Thus 14 is the least multiple of 7 after 11.

(2) Finding the greatest multiple of 7 before 90.

For finding this, divide 90 by 7, and then multiply the quotient thus obtained by 7.

  ⇒ Divide 90 by 7. We get quotient 12.

  ⇒ Multiply 12 by 7. We get 84.

Thus 84 is the greatest multiple of 7 before 90.

(3) Let the multiples of 7 be in an AP.

First term = $a$ = 14

nth term = $\displaystyle a_n$ = 84

common difference = $d$ = 7

Here, value of n is the answer to the question, so,

$\displaystyle n=\frac{a_n-a}{d}+1 \\ \\ \\ n=\frac{84-14}{7}+1 \\ \\ \\ n=\frac{70}{7}+1 \\ \\ \\ n=10+1 \\ \\ \\ n=\boxed{\bold{11}}$

Thus, there are 11 nos. between 11 and 90 which are divisible by 7.