1 minute = 60 seconds

$\frac{1}{4}$ of a minute is $\frac{1}{4}\times 60=15$ seconds

$33\frac{1}{3}=\frac{3\left(33\right)+1}{3}=\frac{99+1}{3}=\frac{100}{3}$

$\frac{33}{121}=\frac{\text{/}11\times 3}{\text{/}11\times 11}=\frac{3}{11}$

$5\frac{1}{6}-3\frac{1}{4}=\frac{31}{6}-\frac{13}{4}=\frac{62-39}{12}\text{(LCM of 6 and 4 is 12)}=\frac{23}{12}=1\frac{11}{12}$

Fraction of book read by Arun  =$\frac{3}{8}+\frac{1}{4}$ $=\frac{3}{8}+\frac{1\times 2}{4\times 2}\text{(LCM of 8 and 4 is 8)}=\frac{3+2}{8}=\frac{5}{8}$
$\therefore$ Fraction of book remaining will be
$=1-\frac{5}{8}=\frac{8-5}{8}=\frac{3}{8}$
$\therefore$ Fraction of book remaining will be $\frac{3}{8}$.

Given that 

The product of two numbers  = 1

One of the numbers = $\frac{2}{3}$
The product of any fraction with its multiplicative inverse is always equal to 1.

Multiplicative inverse of  $\frac{2}{3}$ is  $\frac{3}{2}$

$\Rightarrow$  $\frac{2}{3}\times \frac{3}{2}$ = 1
$\therefore$ The other number is = $\frac{3}{2}$

$2\frac{1}{4}\text{of}2\frac{2}{3}$

$=\frac{9}{4}\times \frac{8}{3}$

$=\frac{9\times 8}{4\times 3}$

$=\frac{72}{12}$

$=6$

As per the question,

Asha read $\frac{1}{4}$ of a book.

Number of pages in the book = 72

Number of pages she read
$=\frac{1}{4}\times 72=18$ 

Total volume of tank = 1680 L

Volume of tank when it is $\frac{4}{7}$ full$=\frac{4}{7}\times 1680=960$ L

Weight of 1 carton of apple juice is,

$=49\frac{1}{2}÷18$

$=\frac{99}{2}÷\frac{18}{1}$

$=\frac{99}{2}\times \frac{1}{18}=\frac{11}{4}=2\frac{3}{4}$ kg