Amrit had some sugar at first. He used 275 g of sugar to bake some muffins and $\frac{3}{5}$ of the remaining sugar to bake some cookies. In the end, he had $\frac{1}{8}$ of the sugar left. How much sugar did he have at first? Ans: ___

1. Find the fraction of the remaining sugar that is left in the end.

Fraction of remaining sugar left = $1 - \frac{3}{5} = \frac{2}{5}$

2. Equate the leftover amount in terms of the remainder and the total, and make the numerators equal to compare units.

We are given that the leftover sugar is $\frac{1}{8}$ of the total sugar.
So, $\frac{2}{5}$ of the remainder = $\frac{1}{8}$ of the total.
Making the numerators the same:
$\frac{2}{5}$ of the remainder = $\frac{2}{16}$ of the total.
This means the remainder is $5$ units and the total is $16$ units.

3. Find the number of units used for muffins and calculate the total amount of sugar.

Units used for muffins = Total units - Remainder units
$= 16 - 5 = 11$ units

$11$ units $= 275$ g
$1$ unit $= 275 \div 11 = 25$ g
Total sugar ($16$ units) $= 16 \times 25 = 400$ g