Question

the product of 2 teo digit number is 1470 the product of their ones digits is 10 and the product of their tens dogit is 12 find the two numbers pls solve it by explanation ​

Answer 1

Let the unit digit in the number be x, then product of digits is 12, the ten's digit in the number is

x

12

.

∴ The value of the number =10×

x

12

+x=

x

120

+x

⇒ On reversing the digits, unit's digit becomes ten's digit and ten's digit becomes unit's digit and its value will become 10x+

x

12

Accroding to the question,

⇒ 10x+

x

12

=

x

120

+x+36

⇒ 9x=

x

120−12

+36

⇒ 9x=

x

108

+36

⇒ 9x

2

=108+36x

⇒ 9x

2

−36x−108=0

⇒ x

2

−4x−12=0

⇒ x

2

−6x+2x−12=0

⇒ x(x−6)+2(x−6)=0

⇒ (x−6)(x+2)=0

⇒ x=6 and x=−2

We can not have negative number in unit place

∴ 6 is unit's place and in tens place we have

6

12

=2

∴ The required number =26

Have a nice day mate ❤️