Mathematics
Seven times a two digit number is equal to four times the number obtained by reversing the order of digits. Find the number, if the difference between its digits is 3.
Linear Equations
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Answer
Let the digit at tens place be x and the digit at unit place be y.
Number = 10x + y
Number on reversing the digits = 10y + x
And, the difference between the digits = x - y or y - x
Given:
⇒ 7(10x + y) = 4(10y + x)
⇒ 70x + 7y = 40y + 4x
⇒ 70x - 4x = 40y - 7y
⇒ 66x = 33y
⇒
⇒ y = 2x …………… (1)
x - y = 3 …………… (2)
Or
y - x = 3 …………… (3)
On solving equations (1) and (2), we get:
x - 2x = 3
x = -3
y = 2 * (-3) = -6
Number = 10x + y = 10 * (-3) + (-6) = -30 - 6 = -36
This case gives a result where the digits are negative (-3 and -6), which is not possible for a two-digit number.
On solving equations (1) and (3), we get:
2x - x = 3
x = 3
y = 2 * (3) = 6
Number = 10x + y = 10 * (3) + (6) = 30 + 6 = 36
Hence, the number = 36.
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