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A number is larger than half of 100. It is more than 6 tens and less than 8 tens. The sum of its digits is 9. The tens digit is the double of the one's digit. What is the number?

A number is larger than half of 100. It is more than 6 tens and less than 8 tens. The sum of its digits is 9. The tens digit is the double of the one's digit. What is the number? Correct Answer 63

Concept used:

A two-digit number is formed by the combination of the unit place and the tens place

Calculation:

Let the unit and the tens digit be x and y

Number = 10y + x

Now, A/Q

The tens digit is double of the one's digit

y = 2x      ----(1)

The sum of its digit is 9 

x + y = 9      ----(2)

From the eq (1) and eq (2)

x + 2x = 9

⇒ 3x = 9 

⇒ x = 3

From eq (1), y = 2 × 3 = 6

Number = 10y + x = 10 × 6 + 3 = 63

The number is greater than half of 100 i.e 50 and more than 6 tens i.e 60 and less than 8 tens i.e 80

∴ The required number is 63

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