Question

The digits of the year $2020$ add up to $2$. In how many years has this happened since the year \[\] till this year $2004$?

A.$3$

B.$6$

C.$9$

D.$10$

Answer 1

Hint: Now we need to see the numbers when the digits are added the sum must be $2$. So from $1$ see the numbers such that its sum is $2$. Count all the numbers which have sum $2$ that will be the answer.


Complete step by step solution
Given:
The sum of the digits of year is $2$.

First let us see how many numbers are there from $1$ to $100$ such that the sum of digits is $2$.

The number we have such that the sum of the digits is $2$

$2$, $11$, $20$.

Hence there are three numbers from $0$ to $100$ having the sum of numbers is $2$.

Second let us see how many numbers there are from $100$ to $1000$ such that the sum of digits is $2$.

The number we have such that the sum of the digits is $2$

$110$,$101$$200$.

Hence there are three numbers from \[\] to $1000$ having the sum of numbers is $2$.


Third let us see how many numbers there are from $1000$ to $2000$ such that the sum of digits is $2$.

The number we have such that the sum of the digits is $2$.

$1001$, $1100$, $1010$, $2000$.

Hence there are four numbers from $1000$ to $2000$ having the sum of numbers is $2$.

From $2001$ to $2004$ there are no numbers having sum as $2$.

Total from \[\]to $2004$ there are $10$ elements having the digit sum as $2$.


Note: $2$in year is nothing but $0002$ years, $11$in year is $0011$, $20$in year is \[\], $101$ in year is $0101$, $110$ in year $0110$, $200$ in year $0200$.