Question

In a two digit number if it is known that its unit digit exceed its tens digit by 2 and that the product of given number and Sum of its digits is equal to 144. then the number is?​

Answer 1

i think your question is incomplete... as you didnt tell the product..

Answer 2

Answer :

• The number is 24

Given that :

• In a two digit number if it is known that it's unit digit exceed its tens digit by 2 and that the product of given number
• Sum of digits is equal to 144

To find :

• Number

Solution :

• Let tens digit number be x

In a two digit number if it is known that its unit digit exceed its tens digit by 2 so,

• Let the units digits number be x + 2

Then,

• 10x + x + 2
• 11x + 2

According to question :

The product of given number and Sum of its digits is equal to 144

➺ (11x + 2) (x + x + 2) = 144

➺ (11x + 2) (2x + 2) = 144

➺ (11x + 2) (x + 1) = 144/2

➺ (11x + 2) (x + 1) = 72

➺ 11x² + 13 - 70 = 0

➺ 11x² - 22x + 35x - 70 = 0

➺ 11x(x - 2) + 35(x - 2) = 0

➺ (x - 2) (11x + 35) = 0

➺ x = 2

Finding the number :

➺ 11x + 2

➺ 11(2) + 2

➺ 22 + 2

➺ 24

Hence, The number is 24.

Verification :

➺ (11x + 2) (x + x + 2) = 144

➺ (11(2) + 2) (2 + 2 + 2) = 144

➺ (22 + 2) (6) = 144

➺ 24 × 6 = 144

➺ 144 = 144

Hence , Verified