Question
When the digits of a two-digit number are interchanged,
the new number becomes 24 more than 180% of the original number. If the sum of the digits is 6, find the original number.Solution
Let the unit digit and tens digit of the original number be ‘y’ and ‘x’, respectively.
Original number = (10x + y)
According to the data given:
10y + x = (9/5) × (10x + y) + 24
Multiplying both sides by 5,
50y + 5x = 90x + 9y + 120
⇒ 85x − 41y = −120 …. (I)
And, x + y = 6 …. (II)
From (II), x = 6 − y. Substitute in (I):
85(6 − y) − 41y = −120
510 − 126y = −120
126y = 630
y = 5
Then x = 1.
So, original number = 10 × 1 + 5 = 15.
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