Linear Equations-algebraic method-eleventh grade-3

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A number consists of two digits, one of which is double the other.
If 18 be added to the number, digits are reversed. Find the number.

Solution: Let x be the smaller digit. Then the greater digit is 2x

Therefore, [10 (x) + 2x] + 18 = 10(2x) + x

i.e. 12x + 18 = 21x

Implies, 21x – 12x = 18 [since 10(2x) + x = 21x]

i.e. 9x = 18, or x = 2

Hence the number is 10 (x) + 2x = 12x = 12 X 2 = 24

Verification: 24 + 18 = 42

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