Question

deepa typed the first n natural numbers on a keyboard without any space. if she had to press the numberd keys 1692 times, find n ?

Answer 1

hello buddy
first of all your question impressed me...
Here is your answer
(1).There are 9 single digit natural numbers and we should press the number for 9 times..
So remaining natural numbers can be obtained by pressing 1683 times..
(2).There are 90 double digit natural numbers and for each number we should press 2 times i.e for 90 natural numbers we should press number key for 90×2=180times..
So remaining natural numbers can be obtained by pressing 1503 times...
(3).Now let the number of triple digit natural numbers as x (since to type 900 triple digit natural numbers we should type 2700 but we have only 1503 times.) and we should press each number for 3 times.i.e X×3 =3x
No of triple digit natural numbers which are obtained by pressing number keys are
3x=1503
x=1503/3
x=501

Therefore the value of n is 9+90+501 i.e 600.

Hope it helps ..!