Question

The tens digit in a two digit number is 4 times the other digit. If you interchange the digits and add the new number to the original number, we get 110. What is the original number ?

Answer 1

here is your answer

Step-by-step explanation:

Let the digit in the unit place be x. Then, tens place be 4x

so, the two digit number is 10×4x+x

with interchanging of the digits, the number will be 10 × x + 4x

According to the question,

10x + 4x + 4ox + x = 110

or, 55x = 110

or, x = 110/55

or, x = 2

Hence, the original number = 40x + x

= 40×2+2 = 80 + 2 = 82.

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Answer 2

Step-by-step explanation:

Let,

• Units digit = x
• Tens digit = 4x

★ Original number = 10 (4x) + x

⇒ 40x + x

⇒ 41x

★ Interchange the digits, new number :

⇒ 10 (x) + 4x

⇒ 10x + 4x

⇒ 14x

★ According to the Question :

When, add the new number to the original number, we get 110.

So,

Original number + New number = 110

⇒ 41x + 14x = 110

⇒ 55x = 110

⇒ x = 110/55

⇒ x = 2

Units digit = 2

• Tens digit = 4x

⇒ 4 (2)

⇒ 8

Tens digit = 8

The Original number = 82

Therefore, The Original number = 82.

★ Verification :

Original number = 41x = 41 × 2 = 82

Interchange the digits, new number = 14x = 14 × 2 = 28

⇒ 82 + 28 = 110

∴ The Original number = 82