The product of 2-digit numbers is 1675. The product of their ones digit is 35 and that of their tens digit is 12. Find the number..

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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.

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The Nos are 25 & 67

Unit digits are 5 & 7 (As Product is 35);  Tens digits are a & 12/a (As prod is 12).  Therefore, required No. are 10a+5 & 120/a + 7  :   Now solve  (10a+5) (120/a+7) = 1675 

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