Razwan is drinking a glass of mango juice. He drinks $\frac{3}{5}$ of it now and $\frac{1}{4}$ of the remaining amount after studying. What fraction of the juice does he have left? $\newline$ A. $30\%$ $\newline$ B. $\frac{1}{10}$ $\newline$ C $\frac{1}{5}$ $\newline$ D $\frac{3}{10}$

Full solution

Q. Razwan is drinking a glass of mango juice. He drinks

\frac{3}{5}

of it now and

\frac{1}{4}

of the remaining amount after studying. What fraction of the juice does he have left?

\newline

30\%

\newline

\frac{1}{10}

\newline

\frac{1}{5}

\newline

\frac{3}{10}

Calculate Remaining Fraction: Razwan drinks $\frac{3}{5}$ of the juice, so we need to calculate the remaining fraction of the juice after this first action. $\newline$ Remaining juice after drinking $\frac{3}{5} = 1 - \frac{3}{5} = \frac{2}{5}$ .
Calculate $\frac{1}{4}$ of Remaining: Now, Razwan drinks $\frac{1}{4}$ of the remaining juice. To find out how much that is, we need to calculate $\frac{1}{4}$ of $\frac{2}{5}$ . $\newline$ $\frac{1}{4}$ of $\frac{2}{5}$ = $(\frac{1}{4}) \times (\frac{2}{5})$ = $\frac{2}{20}$ = $\frac{1}{10}$ .
Subtract $1$ / $10$ from Remaining: After drinking $\frac{1}{10}$ of the remaining juice, we need to subtract this amount from the remaining juice to find out how much is left. $\newline$ Remaining juice after the second drink = $\frac{2}{5} - \frac{1}{10}$ . $\newline$ To subtract these fractions, they need a common denominator.
Convert to Common Denominator: The common denominator for $5$ and $10$ is $10$ . Convert $\frac{2}{5}$ to a fraction with a denominator of $10$ . $\newline$ $\frac{2}{5} = \frac{(2\times2)}{(5\times2)} = \frac{4}{10}$ .
Subtract Fractions: Now subtract $\frac{1}{10}$ from $\frac{4}{10}$ . $\newline$ Remaining juice = $\frac{4}{10} - \frac{1}{10} = \frac{3}{10}$ .