Bissoy.com
Doctors Medicines MCQs Q&A

The difference between a two-digit number and the number obtained by interchanging the digits is 54. What is the difference between the sum and the difference of the digits of the number if the ratio of the digits of the number is 3 ∶ 1?

The difference between a two-digit number and the number obtained by interchanging the digits is 54. What is the difference between the sum and the difference of the digits of the number if the ratio of the digits of the number is 3 ∶ 1? Correct Answer 6

Given:

The difference between a two-digit number and the number obtained by interchanging the digits is 54.

The ratio of the digits of the number is 1 ∶ 3.

Calculation:

Let the unit digit of the number be x and tenth digit be y

Then the number = 10x + y

When we interchange the digit of the number, new number = 10y + x

Now, according to question (10x + y) - (10y + x) = 54

⇒ 10x + y - 10y - x = 54

⇒ 9x - 9y = 54

⇒ 9(x - y) = 54

⇒ x - y = 6      ----(1)

It is given that x : y = 3 : 1

Then x = 3y      ----(2)

By (1) and (2),

3y - y = 6

⇒ 2y = 6

⇒ y = 3

So x = 3y

⇒ x = 3 × 3

⇒ x = 9

So, unit digit of the number = x = 9 and tenth digit of the number = 3

Now, sum of the digits = 9 + 3 = 12 and difference of digit = 9 - 3 = 6

∴ Difference between the sum and the difference of the digits of the number is 6. 

Related Questions

The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and difference of the digits of the number if the ratio between the digits the number is 1 : 2?
The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54. Consider the following statements: 1. The sum of the two digits of the number can be determined only if the product of the two digits is known. 2. The difference between the two digits of the number can be determined. Which of the above statements is/are correct?
The sum of a two digit number and a number obtained by interchanging the digits is 132. What is the product between the sum and difference of the digits of the number, if the ratio between the digits of the number is 1 : 2?
When a two-digit number is multiplied by the sum of its digits, the product is 424. When the number obtained by interchanging its digits is multiplied by the sum of the digits, the result is 280. The sum of the digits of the given number is:
When a two digit number ab, where b > a, is multiplied by the sum of its digits, the number 52 is obtained. When the number obtained by interchanging the digits of the given number is multiplied by the sum of its digits, the number is 124. The value of (14a - 3b) is:
Sum of the digits of a 2-digit number is 7. If number obtained by interchanging the digits is 9 more than the original number, then what is the sum of the squares of the digits of the number?
In a 4-digit number, the sum of the first two digits is equal to that of last two digits. The sum of the first and last digits is equal to third digit. Finally, the sum of the second and fourth digits is twice the sum of the other two digits. What is the third digit of the number?
The sum of a two digit number and the number obtained by interchanging its digits is 165. If the difference between the digits is 3, then what is the product of the digits?
If a number of two digits is k times the sum of its digits, then the number formed by interchanging the digits is the sum of the digits multiplied by :