The sum of the digits of a two-digit number is 9. The number is 6 times the unit digit. Find the number.
please correct answer today is my exam
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Answer:
The required two digit number is 36.
Step-by-step-explanation:
Let the digit at tens place be x.
And the digit at units place be y.
∴ The two-digit number = xy = 10x + y
From the first condition,
x + y = 9
⇒ x = 9 - y
⇒ x = - y + 9 - - - ( 1 )
From the second condition,
10x + y = 6y
⇒ 10x = 6y - y
⇒ 10x = 5y
⇒ 10 ( - y + 9 ) = 5y - - - [ From ( 1 ) ]
⇒ - 10y + 90 = 5y
⇒ 90 = 5y + 10y
⇒ 15y = 90
⇒ y = 90 ÷ 15
⇒ y = 6
∴ The unit digit = 6
By substituting y = 6 in equation ( 1 ), we get,
x = - y + 9
⇒ x = - 6 + 9
⇒ x = 3
∴ The tens digit = 3
Now,
The two-digit number = 10x + y
⇒ The two-digit number = 10 * 3 + 6
⇒ The two-digit number = 30 + 6
⇒ The two-digit number = 36
∴ The required two digit number is 36.
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