Question

the product of two 2-digit numbers is 1675. the product of their ones digits is 35 and that of their digits is 12 . find the numbers.

Answer 1

Let the number be ‘10a + b’ and ‘10c + d’.

Given bd = 35, which can only be written as a product of two single digits as 5×7.

So, either b = 7 and d = 5 or d = 5 or b = 7.

Also given ac = 12, which means either 3×4 or 2×6.
 
So, either a = 3 and c = 4; or a = 4 and c = 3; or a = 6 and c = 2; or a = 2 and c = 6.  

Also, (10a + b)(10c + d) = 100ac + 10(ad + bc) + bd
= 1200 + 10(ad + bc) + 35 = 1235 + 10(ad+bc) = 1675 

Hence, ad + bc = 44 = 30 + 14 = 6 × 5  + 7 × 2

Hence, the number are 67 and 25.