Question

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?

Accepted Answer

B. Let middle digit be $b$. Leftmost digit $a = 2b$, rightmost $c = 3b$. Number is $100(2b) + 10b + 3b = 213b$. For $b=1$: 213. Rearrangements minus 213 check for 198 difference: $426 - 213 = 213 
eq 198$. For $b=2$: 426. Rearrangement $624 - 426 = 198$. So $b = 2$. Middle digit is 2.

Three-Digit Profit Digits

Explanation

Practise this under exam conditions