Question

The sum of the numbers $2053$ and $412$ which are in the scale of seven is

• A. $(929{)}_{10}$
• B. $(939{)}_{10}$
• C. $(959{)}_{10}$
• D. none of these

Answer 1

The correct option is A $(929{)}_{10}$

Assuming the given numbers $2053$ and $412$ are in base $7$ number system

Converting ${\left(2053\right)}_7$ to base 10 representation = $2\times 7^3+0\times 7^2+5\times 7+3\times 7^0$ = ${\left(724\right)}_{10}$

Similarly, converting ${\left(412\right)}_7$ to base 10 representation = $4\times 7^2+1\times 7+2\times 7^0={\left(205\right)}_{10}$

$\Rightarrow {\left(724\right)}_{10}+{\left(205\right)}_{10}={\left(929\right)}_{10}$