Question

A number when divided by 11 leaves remainder 5. If the same number is multiplied by 8 and 3 is added to it, then what will be the remainder when it is divided by 11?
1. 7
2. 10
3. 15
4. 3

Answer 1

Correct Answer - Option 2 : 10

Given:

Remainder on dividing the number by 11 = 5

Formula Used:

Dividend = Divisor × Quotient + Remainder

Calculations:

Let the quotient for dividing the number by 11 be q.

⇒ Number = 11 × q + 5 

When this number is multiplied by 8 and 3 is added, 

New number = 8 × (11q + 5) + 3

⇒ New number = 88q + 43

⇒ New number = (8 × 11q + 33) + 10 = 11 × (8q + 3) + 10

On dividing this number by 11,

Remainder = 10

∴ The remainder when given number is divided by 11 is 10.