Question

What is the sum of all those numbers between 10 and 99, both inclusive, that leave a remainder of 15 upon
division by 21?​

Answer 1

SOLUTION

TO DETERMINE

The sum of all those numbers between 10 and 99, both inclusive, that leave a remainder of 15 upon division by 21

EVALUATION

Let the number = m and quotient = n

Now

Dividend = Quotient × Divisor + Remainder

⇒ m = 21n + 15

Where n = 0 , 1 , 2 , 3 , 4...

Putting

n = 0 we get m = 15

n = 1 we get m = 36

n = 2 we get m = 57

n = 3 we get m = 78

n = 4 we get m = 99

n = 5 we get m = 120

Since the numbers between 10 and 99, both inclusive

So the numbers are 15 , 36 , 57 , 78 , 99

Hence the required sum

= 15 + 36 + 57 + 78 + 99

= 285

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