Mathematics
A number of two digits exceeds four times the sum of its digits by 6 and it is increased by 9 on reversing the digits. Find the number.
Linear Equations
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Answer
Let's consider the digits at ten's place as x and let the digit at unit's place be y.
Number = 10 × x + y = 10x + y,
On reversing digits the number is = 10 × y + x = 10y + x.
According to first condition, we have
⇒ 10x + y - [4(x + y)] = 6
⇒ 10x + y - 4x - 4y = 6
⇒ 10x - 4x + y - 4y = 6
⇒ 6x - 3y = 6
⇒ 2x - y = 2 ……(i)
According to second condition, we have
⇒ 10x + y + 9 = 10y + x
⇒ 10x - x + y - 10y = -9
⇒ 9x - 9y = -9
⇒ x - y = -1
⇒ y - x = 1 ……(ii)
Adding eq. (i) and (ii) we get,
⇒ 2x - y + (y - x) = 2 + 1
⇒ x = 3.
Substituting value of x in (ii) we get,
⇒ y - 3 = 1
⇒ y = 4.
Number = 10 × x + y = 10 × 3 + 4 = 30 + 4 = 34.
Hence, number = 34.
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