Question

A two digit number is obtained by either multiplying sum of the digits by 8 and adding 1 or by multiplying the difference of the digits by 13 and adding 2. The number is 

(a) 14 

(b) 42 

(c) 24 

(d) 41

Answer 1

(d) 41

Let the two digit number be 10x + y. 

According to the question,

10x + y = 8(x + y) + 1  \(\Rightarrow\) 2x – 7y = 1 ….......(i)

and 10x + y = 13(x – y) + 2 \(\Rightarrow\) 3x – 14y = –2 ...…(ii)

Now we can get x and y.