Advertisements
Advertisements
Question
In a two-digit number, the ten’s digit is bigger. The product of the digits is 27 and the difference between two digits is 6. Find the number.
Advertisements
Solution
Given, the difference between the two digits is 6 and the ten’s digit is bigger than the unit’s digit.
So, let the unit’s digit be x and ten’s digit be (x + 6).
From the given condition, we have:
x(x + 6) = 27
x2 + 6x – 27 = 0
x2 + 9x – 3x – 27 = 0
x(x + 9) – 3(x + 9) = 0
(x + 9)(x – 3) = 0
x = –9, 3
Since, the digits of a number cannot be negative.
So, x = 3.
Unit’s digit = 3
Ten’s digit = 9
Thus, the number is 93.
RELATED QUESTIONS
A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.
The product of two consecutive integers is 56. Find the integers.
The sum of a number and its reciprocal is 4.25. Find the number.
Two natural numbers differ by 3. Find the numbers, if the sum of their reciprocals is `7/10`.
The sum of the squares of two consecutive positive even numbers is 52. Find the numbers.
The denominator of a positive fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2.9; find the fraction.
The sum of two natural numbers is 5 and the sum of their reciprocals is `5/6`, the numbers are ______.
The product of two consecutive even whole numbers is 24, the numbers are ______.
The product of two whole numbers, each greater than 4, is 35; the numbers are ______.
If 18 is added to a two-digit number, its digits are reversed. If the product of the digits of the number is 24, the number is ______.
