Two number when divided by 17, leaves remainder 13 and 11 respectively. If the sum of those two numbers is divided by 17, the remainder will be ?

Solution(By Examveda Team)

Dividend = divisor × quotient + remainder
$$\eqalign{ & {\text{First number }} \cr & \Rightarrow {\text{ }}\left( {17 \times {\text{n}}} \right) + 13 \cr & {\text{Let n = 1}} \cr & \Rightarrow (17 \times 1) + 13 \cr & \Rightarrow 30 \cr & {\text{second number }} \cr & \Rightarrow {\text{ }}\left( {17 \times {\text{n}}} \right) + 11 \cr & \Rightarrow (17 \times 1) + 11 \cr & \Rightarrow 28 \cr & {\text{According to question}} \cr & = \frac{{30 + 28}}{{17}} \cr & = \frac{{58}}{{17}} \cr & \Rightarrow {\text{remainder = 7}} \cr} $$

Alternate :
Divisor = 1^st remainder + 2^nd remainder - 3^rd remainder
$$\eqalign{ & 17 = {\text{ }}13 + 11 - {\text{3rd remainder}} \cr & {\text{3rd remainder}} = 24 - 17 = 7 \cr} $$