Question

Find the number x if (a)22% of X is 26.4 (b) 8.4% of X is 42 (c) ½% of X is 50 (d) x% of 1800 is 9

Answer 1

To find : value of $x$ in following

a) $22\% \ of x \ is \ 26.4$   b) $8.4\% \ of \ x \ is \ 42$    c)$\frac{1}{2}\% \ of \ x \ is \ 50$  d) $x\% \ of \ 1800 \ is \ 9$

Solution :

• A percentage is a fraction of an amount expressed as a particular number of hundredths of that amount.
• It is denoted by means %.
• Fractions can be converted into percentages and vice-versa.
• Percentages are reversible.

        a )$22\% \ of x \ is \ 26.4$

            $\begin{array}{l}22 \% \text { of } x = 26.4 \\\frac{22}{100} \times x = 26.4 \\x =\frac{26.4 \times 50}{11} \\x = 120\end{array}$

       b) $8.4\% \ of \ x \ is \ 42$  

            $\frac{8.4}{100} \times x = 42 \\ x = \frac{42\times 100}{8.4} \\x = 500$

       c) $\frac{1}{2}\% \ of \ x \ is \ 50$  

          $\frac{0.5}{100}\times x = 50 \\x = \frac{50\times 100}{0.5} \\x = 10000$

       d) $x\% \ of \ 1800 \ is \ 9$

         $\frac{x}{100} \times 1800 =9 \\x = \frac{9\times 100}{1800} \\x = \frac{1}{2} \\or \ x = 0.5$

Hence, the value of $x$ for a) , b) , c) and d) will be $120 , 500, 10000 \ and \ 0.5$ respectively .

Answer 2

given: $\text { a) } 22 \% \text { of } x \text { is } 26.4\text { b) } 8.4 \% \text { of } x \text { is } 42\text { c) }^{\frac{1}{2}} \% \text { of } x \text { is } 50\text { d) } x \% \text { of } 1800 \text { is } 9$

We have to find the value of '$x$'.

As we know that a percentage is a fraction of an amount expressed as a particular number of hundredths of that amount.

We are solving in the following way:

We have,

$\text { a) } 22 \% \text { of } x \text { is } 26.4$

$=>x\times\frac{22}{100} =26.4\\\\=>22x=26.4\times100\\=>22x=2640\\\\=>x=\frac{2640}{22} \\\\=>x=120$

$b)x\times\frac{8.4}{100} =42\\\\=>8.4x=42\times100\\=>8.4x=4200\\\\=>x=\frac{4200}{8.4} \\\\=>x=500$

$c)x\times\frac{0.5}{100} =50\\\\=>0.5x=50\times100\\=>0.5x=5000\\\\=>x=\frac{5000}{0.5} \\\\=>x=10,000$

$d)\frac{x}{100} \times1800=9\\\\=>1800x=9\times100\\\\=>1800x=900\\\\=>x=\frac{900}{1800} \\\\=>x=\frac{1}{2} \\\\=>x=0.5$

Hence, the value of '$x$' will be$120,500,(10,000),0.5$