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# In a three-digit number, the digit in the unit's place is four times the digit in the hundred's place. If the digit in the unit's place and the ten's place are interchanged, the new number so formed is 18 more than the original number. If the digit in the hundreds place is one-third of the digit in the ten's place, then what is 25% of the original number?

 A) 67 B) 84 C) 137 D) Couldn't be determined

 A) 67

Let hundred's digit = x

Then unit's digit = 4x and ten's digit = 3x

Number = 100x + 30x + 4x = 134x

Again, hundred's digit = x

Ten's digit = 4x and unit's digit = 3x

Number = 100x + 40x + 3x = 143x

According to the question,

143x -134X = 18 => 9x = 18

x = 2

Original number = 134x = 134 x 2 = 268

25% of original number = $$\Large 268 \times \frac{25}{100} = 67$$

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