[ Percentage and ratio problems ]

How many pounds of grain need to be milled, so that after paying for the work at $-10 \%$ of the milling - exactly 100 pounds of flour remain? There are no losses during milling.

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Think about what part of the payment will be from the final revenue, not the initial one.

## Solution

The 100 pounds that remain constitute (100 - 10)%, i.e., 90%. Thus, 100 pounds is 9/10. From this, we can find the initial amount of grain \( A \). \( A = 100 \) pounds × 10/9. Therefore, \( A = 1000 / 9 \) pounds or \( 111 + 1 / 9 \) pounds. Indeed, \( (9 / 10) \times (111 + 1 / 9) \) pounds \( = (9 / 10) \times (1000 / 9) \) pounds \( = 100 \) pounds.

## Answer

\( 111 + 1 / 9 \) pounds.