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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

xy=3366\dfrac{x}{y} = \dfrac{33}{66}

⇒ 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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