When digits of a first two-digit number are reversed, then the resulting number will become 75% of second two-digit number. The difference of squares of tens digit and units digit of the second number is 20. Find the first number.
Question
When digits of a first two-digit number are reversed, then the resulting number will become 75% of second two-digit number. The difference of squares of tens digit and units digit of the second number is 20. Find the first number.
Solution
Let's break down the problem step by step:
Step 1: Let's assume the first two-digit number is represented as "AB", where A is the tens digit and B is the units digit.
Step 2: According to the problem, when the digits of the first number are reversed, the resulting number becomes 75% of the second two-digit number. This can be represented as:
(10B + A) = 0.75 * (10A + B)
Step 3: Simplifying the equation, we get:
10B + A = 7.5A + 0.75B
Step 4: Rearranging the equation, we get:
10B - 0.75B = 7.5A - A
9.25B = 6.5A
Step 5: We are also given that the difference of squares of the tens digit and units digit of the second number is 20. This can be represented as:
A^2 - B^2 = 20
Step 6: Simplifying the equation, we get:
(A + B)(A - B) = 20
Step 7: Now, we need to find the values of A and B that satisfy both equations simultaneously.
By trial and error, we can find that A = 5 and B = 3 satisfy both equations.
Step 8: Therefore, the first two-digit number is 53.
Similar Questions
The units digit of a two-digit number is 1 more than 4 times the tens digit. If the digits are reversed, the new number is 5 more than 3 times the original number. What is the number with the digits reversed?1 pointA. 15B. 29C. 51D. 92
The digit at the unit’s place of a two-digit number is increased by 50%. And the digit at the ten’s place of the same number is increased by 100%. Now, we find the new numbers is 33 more than original number. Find the original number.
The difference between the digits of a two-digit number is 4 and the digit in the unit’s place is one-third of the digit in the tenth’s place. what is the two -digit number?
On reversing the digits of a two digit number, number obtained is 9 less than three times theoriginal number. If difference of these two numbers is 45, find the original number.
The sum of the digits of a two digit number is 8 and the difference between the number and thatformed by reversing the digits is 18. Find the number.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.