Question

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

Answer 1

Given:

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

To find:

Find the number

Solution:

From given, we have,

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

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

Given bd = 35 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.