Mathematics
A number of two digits exceeds four times the sum of its digits by 6, and the number is increased by 9 on reversing its digits. Find the number.
Linear Equations
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Answer
Let the ten's and unit's digit of required number be x and y respectively.
Number = 10x + y
Given,
A number of two digits exceeds four times the sum of its digits by 6.
⇒ 10x + y - 4(x + y) = 6
⇒ 10x + y - 4x - 4y = 6
⇒ 6x - 3y = 6 …..(1)
Number obtained by reversing the digits = 10y + x
Given,
Number is increased by 9 on reversing its digits.
⇒ 10y + x = 10x + y + 9
⇒ 10y - y + x - 10x = 9
⇒ 9y - 9x = 9
⇒ y - x = 1
⇒ x = y - 1 …..(2)
Substituting the value of x from equation (2) in equation 1,
⇒ 6(y - 1) - 3y = 6
⇒ 6y - 6 - 3y = 6
⇒ 3y - 6 = 6
⇒ 3y = 6 + 6
⇒ 3y = 12
⇒ y =
⇒ y = 4.
Substituting value of y in equation (2), we get :
⇒ x = 4 - 1
⇒ x = 3.
Number = 10x + y
= 10 × 3 + 4
= 34.
Hence, the number is 34.
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