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Question 7 : Fatima found that the profit earned by the Bala dosa stall today is a three-digit number. She also noticed that the middle digit is half of the leftmost digit, while the rightmost digit is three times the middle digit. She then randomly interchanged the digits and obtained a different number. This number was more than the original number by 198.

What was the middle digit of the profit amount?

- 2
- 1
- 6
- This cannot be solved with only the given information
- 8

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Given that there is a three-digit number.

The middle digit is half of the leftmost digit

The rightmost digit is three times the middle number.

The possible digits for the middle number are only 1, 2, 3, the possible three digit numbers are 213, 426, and 639

If we add 198 to the above numbers we should get the number that has the same digits of the original number.

213 + 198 = 411 (not possible)

426 + 198 = 624 (possible)

639 + 198 = 837 (not possible)

Therefore, the possible number is 426. The middle number is 2

Choice A is the correct answer.

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