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

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by mehtaaarti1

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by mehtaaarti1

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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.

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

⇒

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.

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.