The difference between two digits of a two-digit number is 4, where th

1.	The difference between two digits of a two-digit number is 4, where the unit place number is great than the tenth-place number. If digits are interchanged and the resulting number is added with the original number get 66 as result. What is the original number?1. 152. 513. 624. 26
Answer» Correct Answer - Option 1 : 15 Given: The difference between two digits of a two-digit number is 4, where the unit place number is great than the tenth-place number. If digits are interchanged and the resulting number is added with the original number get 66 as result. Concept Used: 1.) Linear equation of one variable 2.) In a two digit number if the unit place number is p and the tenth place number is q then the number should be (10q + p) Calculation: Let, the tenth-place number is x The unit place number is great than the tenth-place number and difference between them is 4 Unit place number is (x + 4) The number is {10x + (x + 4)} = (11x + 4) When the digits interchange their position the number will become {10 × (x + 4) + x} ⇒ (11x + 40) Accordingly, (11x + 4) + (11x + 40) = 66 ⇒ 22x + 44 = 66 ⇒ 22x = 66 – 44 ⇒ 22x = 22 ⇒ x = 1 The tenth-place digit is 1 and the unit place digit is (1 + 4) = 5 ∴ The original number is {(1 × 10) + 5} = 15

The difference between two digits of a two-digit number is 4, where the unit place number is great than the tenth-place number. If digits are interchanged and the resulting number is added with the original number get 66 as result. What is the original number?1. 152. 513. 624. 26

Answer» Correct Answer - Option 1 : 15

Given:

The difference between two digits of a two-digit number is 4, where the unit place number is great than the tenth-place number.

If digits are interchanged and the resulting number is added with the original number get 66 as result.

Concept Used:

1.) Linear equation of one variable

2.) In a two digit number if the unit place number is p and the tenth place number is q then the number should be (10q + p)

Calculation:

Let, the tenth-place number is x

The unit place number is great than the tenth-place number and difference between them is 4

Unit place number is (x + 4)

The number is {10x + (x + 4)} = (11x + 4)

When the digits interchange their position the number will become {10 × (x + 4) + x}

⇒ (11x + 40)

Accordingly,

(11x + 4) + (11x + 40) = 66

⇒ 22x + 44 = 66

⇒ 22x = 66 – 44

⇒ 22x = 22

⇒ x = 1

The tenth-place digit is 1 and the unit place digit is (1 + 4) = 5

∴ The original number is {(1 × 10) + 5} = 15