Question

In a certain code language, if the value of $38+15=66$ and $29+36=99$, then what is the value of $82+44$?
(a) 77
(b) 88
(c) 80
(d) 92

Answer 1

Hint: We start solving this problem by writing the number on the right-hand side of the result into the multiplication of two numbers. We then write those numbers as the sum of the digits present on the left-hand side to get the relation between the digits involving the sum for both the given results. We then use that relationship for the result of $82+44$ in a similar way to get the required answer.

Complete step-by-step solution
According to the problem, we are given that the values are defined in a certain code language as $38+15=66$ and $29+36=99$. We need to find the value of $82+44$.
Now, we need to find the relation between the three numbers present at $38+15=66$.
So, we have $38+15=66$.
$\Rightarrow 38+15=11\times 6$.
$\Rightarrow 38+15=\left( 3+8 \right)\times \left( 1+5 \right)$ ---(1).
Now, let us find the relation between the three numbers present in $29+36=99$.
$\Rightarrow 29+36=11\times 9$.
$\Rightarrow 29+36=\left( 2+9 \right)\times \left( 3+6 \right)$ ---(2).
From equations (1) and (2), we can see that the sum of two numbers in the form of $mn$ and $pq$ is defined as $mn+pq=\left( m+n \right)\times \left( p+q \right)$.
Let us use this result for finding the value of $82+44$.
$\Rightarrow 82+44=\left( 8+2 \right)\times \left( 4+4 \right)$.
$\Rightarrow 82+44=10\times 8$.
$\Rightarrow 82+44=80$.
So, we have found the value of $82+44$ as 80.
∴ The correct option for the given problem is (c).

Note: We should know that the given set of results can give different answers for a different type of relations performed by the setter of the question. We can also get another result as shown below:
We have $38+15=66$.
$\Rightarrow 38+15=36+30$.
$\Rightarrow 38+15=\left( 38-2 \right)+\left( 15\times 2 \right)$ ---(3).
Now, we have $29+36=99$.
$\Rightarrow 29+36=27+72$.
$\Rightarrow 29+36=\left( 29-2 \right)+\left( 36\times 2 \right)$ ---(2).
From equations (1) and (2), we can see that the sum of two numbers in the form of $mn$ and $pq$ is defined as $mn+pq=\left( mn-2 \right)+\left( pq\times 2 \right)$.
Let us use this result for finding the value of $82+44$.
$\Rightarrow 82+44=\left( 82-2 \right)+\left( 44\times 2 \right)$.
$\Rightarrow 82+44=80+88$.
$\Rightarrow 82+44=168$.
So, we need to perform different methods to get answers as mentioned in the problems.