Question

Which of the following numbers must be added to 5678 to give a reminder 35 when divided by 460?

Answer 1

267 is to be added If correct brainliest I will tell the method if you want

Answer 2

dividend = divisor × quotient + remainder
5678 = 460 ×12 + 158
Here 158 is the remainder. we need the remainder to be 35 by adding a number.
Let the number to be added be x.

Since 158>35, the quotient we will get by dividing  (5678+x) by 460 should be greater than 12. It may be 13, 14, 15 etc. but i am taking the lowest one here i.e.13.

So (5678 +x) = 460 × 13 + 35  (here 35 is remainder)
⇒ 5678 + x -35 = 460 × 13
⇒5643 + x = 460 × 13
⇒x = 460 × 13 - 5643
⇒ x = 337

If you take 14 to be the quotient, you will get x= 797
If you take 15 to be the quotient, you will get x= 1257
If you take 16 to be the quotient, you will get x= 1717  etc....
The x will increase by 460 as you increase the quotient by 1.