Question 56

How many two digit numbers are divisible by 9?

Solution

2 digits numbers which are divisible by 9 are : 18,27,.....,99

Clearly, these numbers form an A.P. with first term, $$a=18$$, last term, $$l=99$$ and common difference, $$d=9$$

Let number of terms be $$n$$

=> Last term of an A.P. = $$l=a+(n-1)d$$

=> $$99=18+(n-1)9$$

=> $$(n-1)9=99-18=81$$

=> $$(n-1)=\frac{81}{9}=9$$

=> $$n=9+1=10$$

Thus, there are 10 two digit numbers that are divisible by 9.

=> Ans - (C)

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