Question

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

Answer 1

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.

Answer 2

on dividing 5678 by 460 we get a remainder of 158 and quotient of 12
 and 12 × 460=5520.
as 158 is more than 35.we need a no that is 35 more than the next multiple of 460
460 ×13=5980.and 35 has to be added to that no.so the req no is 6015.
the difference between 5678 and 6015 is 337
.so 337 must be added to 5678 so that it leaves a remainder of 35 when divided by 460