Mathematics
A number consists of two digits, the difference of whose digits is 5. If 8 times the number is equal to 3 times the number obtained by reversing the digits, find the number.
Linear Equations
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Answer
According to question,
Original number is smaller than the number obtained by reversing its digits.
∴ In original number, unit's digit greater than ten's digit.
Let the ten's and unit's digit of required number be x and y respectively y > x.
Given,
⇒ y - x = 5
⇒ y = x + 5 …..(1)
Number obtained by reversing the digits = (10y + x)
Given,
8 times the number is equal to 3 times the number obtained by reversing the digits.
⇒ 8(10x + y) = 3(10y + x)
⇒ 80x + 8y = 30y + 3x
⇒ 80x - 3x + 8y - 30y = 0
⇒ 77x - 22y = 0 …..(2)
Substituting the value of x from equation (2) in 77x - 22y = 0, we get:
⇒ 77x - 22y = 0
⇒ 77x - 22 × (x + 5) = 0
⇒ 77x - 22x - 110 = 0
⇒ 55x - 110 = 0
⇒ 55x = 110
⇒ x =
⇒ x = 2.
Substituting value of y in equation (2), we get :
⇒ y = x + 5
⇒ y = 2 + 5
⇒ y = 7.
Number = (10x + y) = 10 × 2 + 7 = 27.
Hence, the number is 27.
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