Question

Find the sum of all the two digit numbers which leave the remainder 2 when divided by 5.

Answer 1

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Answer 2

Given:

A statement.

To find:

The sum of all the two-digit numbers that leave the remainder 2 when divided by 5.

Solution:

The sum of all the two-digit numbers that leave the remainder 2 when divided by 5 is 981.

To answer this question, we will follow the following steps:

The required two-digit numbers that leave the remainder 2 when divided by 5 are

12, 17, 22, ..., 97

As there is a common difference i.e. 5 between two consecutive terms, this means, it forms an A.P.

Here

a = 12

d = 5

So,

The total number of terms can be given by using the formula:

nth term = a + (n - 1) d

97 = 12 + (n - 1) 5

97 = 12 + 5n - 5

90 = 5n

18 = n

The sum of 18 terms of an A.P. is given by

$= \frac{n}{2} [2a + (n - 1)d]$

$= \frac{18}{2} [2(12) + (18 - 1)5]$

On solving the above, we get

$= 9(24 + 85)$

$= 9 \times 109$

$= 981$

Hence, the sum of all the two-digit numbers that leave the remainder 2 when divided by 5 is 981.