Question

Rahul wanted to type of first 180 natural numbers, find the number of times he had to press numbered keys
(a) 384
(b) 432
(c) 416
(d) 448

Answer 1

Hint: We will start with counting the number of times a single digit number is pressed. Then we will count the number of times the double digit number is used and finally count the number of times the three-digit number is used.Now add all the values to get the required answer.

Complete step-by-step answer:
It is mentioned in the question that he wants to type the first 180 natural numbers. Let’s first understand natural numbers. So natural numbers are part of the number system which includes all the positive integers from 1 till infinity.
So the first 180 natural numbers include 9 single digit numbers, 90 double digit numbers and 81 three-digit numbers.
Number of times key was pressed for the numbers 1 to 9 \[=1\times 9=9....(1)\]
Number of times key was pressed for the numbers 10 to 99 \[=2\times 90=180....(2)\]
Number of times key was pressed for the numbers 100 to 180 \[=3\times 81=243....(3)\]
Now adding equation (1), equation (2), equation (3) we get,
The number of times Rahul had to press the numbered keys \[=9+180+243=\,432\]
Hence 432 times Rahul pressed the numbered keys to type first 180 natural numbers. So option (b) is the correct option.

Note: First we need to understand the concept of natural numbers. Then we need to understand that for entering single digit numbers we have to press the key one time only for each number whereas for double digit numbers we have to press the key two times for each number and for three-digit numbers we have to press the key three times for each number.