Question

By cross multiplication method, find such a two digit number, where the digital units place is twice the digit at ten's place and the number obtained by Interchanging the digits of the number is 36 more than the original number. Find the original number.

Answer 1

To find the original two-digit number using the cross multiplication method, set up the equation x = 10t + u, where x is the original number, t is the digit in the tens place, and u is the digit in the units place. The equation to solve is 10u + t = 10t + u + 36. By simplifying and solving for t, the original number is found to be 48.

Step-by-step explanation:

To find the original two-digit number using the cross multiplication method, we can set up the following equation:

x = 10t + u

Where x is the original two-digit number, t is the digit in the tens place, and u is the digit in the units place.

According to the given conditions, u = 2t, and the number obtained by interchanging the digits is 36 more than the original number. This gives us the equation:

10u + t = 10t + u + 36

Substituting u = 2t into the equation, we get:

10(2t) + t = 10t + 2t + 36

Simplifying further, we have:

20t + t = 12t + 36

Combining like terms, we get:

21t = 12t + 36

Subtracting 12t from both sides of the equation, we get:

9t = 36

Dividing both sides by 9, we find that t = 4.

Substituting this value back into the equation u = 2t, we get u = 8.

Therefore, the original number is 48.