Chapter 23, Problem 21AR

To determine

(a)

The base under given condition.

Answer to Problem 21AR

$33.33$

Explanation of Solution

Given information:

Rate is given as $60\%$ and percentage is $20$. Need to find base.

Calculation:

As we know the proportion to find percentage is given as

$\frac{P}{B}=\frac{R}{100}$   where, $P=\text{percentage, }B=\text{ base and }R=\text{rate}$

Now, as per the problem statement rate is given as $60\%$. i.e. $R=$$60$.

Also, percentage $P=$$20$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{20}{B}=\frac{60}{100}\text{ {Put }P=20\text{ and }R=60\text{}}\\ \text{Applying cross multiplication,}\\ \Rightarrow 60B=20\times 100\\ \Rightarrow B=\frac{20\times 100}{60}\\ \Rightarrow B=33.33\end{array}$

Hence, we can say that $20$ is $60\%$ of $33.33$.

To determine

(b)

The base under given condition.

Answer to Problem 21AR

$16.46$

Explanation of Solution

Given information:

Rate is given as $24.9\%$ and percentage is $4.1$. Need to find base.

Calculation:

As we know the proportion to find percentage is given as

$\frac{P}{B}=\frac{R}{100}$   where, $P=\text{percentage, }B=\text{ base and }R=\text{rate}$

Now, as per the problem statement rate is given as $24.9\%$. i.e. $R=$$24.9$.

Also, percentage $P=$$4.1$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{4.1}{B}=\frac{24.9}{100}\text{ {Put }P=4.1\text{ and }R=24.9\text{}}\\ \text{Applying cross multiplication,}\\ \Rightarrow 24.9B=4.1\times 100\\ \Rightarrow B=\frac{4.1\times 100}{24.9}\\ \Rightarrow B=16.46\end{array}$

Hence, we can say that $4.1$ is $24.9\%$ of $16.46$.

To determine

(c)

The base under given condition.

Answer to Problem 21AR

$223.68$

Explanation of Solution

Given information:

Rate is given as $152\%$ and percentage is $340$. Need to find base.

Calculation:

As we know the proportion to find percentage is given as

$\frac{P}{B}=\frac{R}{100}$   where, $P=\text{percentage, }B=\text{ base and }R=\text{rate}$

Now, as per the problem statement rate is given as $152\%$. i.e. $R=$$152$.

Also, percentage $P=$$340$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{340}{B}=\frac{152}{100}\text{ {Put }P=340\text{ and }R=152\text{}}\\ \text{Applying cross multiplication,}\\ \Rightarrow 152B=340\times 100\\ \Rightarrow B=\frac{340\times 100}{152}\\ \Rightarrow B=223.68\end{array}$

Hence, we can say that $340$ is $152\%$ of $223.68$.

To determine

(d)

The base under given condition.

Answer to Problem 21AR

$59.97$

Explanation of Solution

Given information:

Rate is given as $73.5\%$ and percentage is $44.08$. Need to find base.

Calculation:

As we know the proportion to find percentage is given as

$\frac{P}{B}=\frac{R}{100}$   where, $P=\text{percentage, }B=\text{ base and }R=\text{rate}$

Now, as per the problem statement rate is given as $73.5\%$. i.e. $R=$$73.5$.

Also, percentage $P=$$44.08$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{44.08}{B}=\frac{73.5}{100}\text{ {Put }P=44.08\text{ and }R=73.5\text{}}\\ \text{Applying cross multiplication,}\\ \Rightarrow 73.5B=44.08\times 100\\ \Rightarrow B=\frac{44.08\times 100}{73.5}\\ \Rightarrow B=59.97\end{array}$

Hence, we can say that $44.08$ is $73.5\%$ of $59.97$.

To determine

(e)

The base under given condition.

Answer to Problem 21AR

$3.90$

Explanation of Solution

Given information:

Rate is given as $238.6\%$ and percentage is $9.3$. Need to find base.

Calculation:

As we know the proportion to find percentage is given as

$\frac{P}{B}=\frac{R}{100}$   where, $P=\text{percentage, }B=\text{ base and }R=\text{rate}$

Now, as per the problem statement rate is given as $238.6\%$. i.e. $R=$$238.6$.

Also, percentage $P=$$9.3$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{9.3}{B}=\frac{238.6}{100}\text{ {Put }P=9.3\text{ and }R=238.6\text{}}\\ \text{Applying cross multiplication,}\\ \Rightarrow 238.6B=9.3\times 100\\ \Rightarrow B=\frac{9.3\times 100}{238.6}\\ \Rightarrow B=3.90\end{array}$

Hence, we can say that $9.3$ is $238.6\%$ of $3.90$.

To determine

(f)

The base under given condition.

Answer to Problem 21AR

$41.18$

Explanation of Solution

Given information:

Rate is given as $2.04\%$ and percentage is $0.84$. Need to find base.

Calculation:

As we know the proportion to find percentage is given as

$\frac{P}{B}=\frac{R}{100}$   where, $P=\text{percentage, }B=\text{ base and }R=\text{rate}$

Now, as per the problem statement rate is given as $2.04\%$. i.e. $R=$$2.04$.

Also, percentage $P=$$0.84$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{0.84}{B}=\frac{2.04}{100}\text{ {Put }P=0.84\text{ and }R=2.04\text{}}\\ \text{Applying cross multiplication,}\\ \Rightarrow 2.04B=0.84\times 100\\ \Rightarrow B=\frac{0.84\times 100}{2.04}\\ \Rightarrow B=41.18\end{array}$

Hence, we can say that $0.84$ is $2.04\%$ of $41.18$.

To determine

(g)

The base under given condition.

Answer to Problem 21AR

$0.61$

Explanation of Solution

Given information:

Rate is given as $123\%$ and percentage is $\frac{3}{4}$. Need to find base.

Calculation:

As we know the proportion to find percentage is given as

$\frac{P}{B}=\frac{R}{100}$   where, $P=\text{percentage, }B=\text{ base and }R=\text{rate}$

Now, as per the problem statement rate is given as $123\%$. i.e. $R=$$123$.

Also, percentage $P=$$\frac{3}{4}$

$=0.75$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{0.75}{B}=\frac{123}{100}\text{ {Put }P=0.75\text{ and }R=123\text{}}\\ \text{Applying cross multiplication,}\\ \Rightarrow 123B=0.75\times 100\\ \Rightarrow B=\frac{0.75\times 100}{123}\\ \Rightarrow B=0.61\end{array}$

Hence, we can say that $\frac{3}{4}$ is $123\%$ of $0.61$.