Chapter 23, Problem 22AR

To determine

(a)

The rate under given condition.

Answer to Problem 22AR

$75\%$

Explanation of Solution

Given information:

Base is given as $24$ and percentage is $18$. Need to find rate(percent).

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 base is given as $24$. i.e. $B=$$24$.

Also, percentage $P=$$18$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{18}{24}=\frac{R}{100}\\ \text{Applying cross multiplication,}\\ \Rightarrow 24R=18\times 100\\ \Rightarrow R=\frac{18\times 100}{24}\\ \Rightarrow R=75\end{array}$

Hence, we can say that $75\%$ of $24$ is $18$.

To determine

(b)

The percentage under given condition.

Answer to Problem 22AR

$15$

Explanation of Solution

Given information:

Rate is given as $30\%$ and base is $50$.

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 $30\%$ i.e. $R=$$30$

Also, base $B=$$50$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{P}{50}=\frac{30}{100}\\ \text{Applying cross multiplication,}\\ \Rightarrow \text{100}P=30\times 50\\ \Rightarrow P=\frac{30\times 50}{100}\\ \Rightarrow P=15\end{array}$

Hence, $30\%$ of $50$ is equal to $15$.

To determine

(c)

The percentage under given condition.

Answer to Problem 22AR

$15.60$

Explanation of Solution

Given information:

Rate is given as $123.8\%$ and base is $12.6$.

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 $123.8\%$ i.e. $R=$$123.8$

Also, base $B=$$12.6$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{P}{12.6}=\frac{123.8}{100}\\ \text{Applying cross multiplication,}\\ \Rightarrow \text{100}P=12.6\times 123.8\\ \Rightarrow P=\frac{12.6\times 123.8}{100}\\ \Rightarrow P=15.60\end{array}$

Hence, $123.8\%$ of $12.6$ is equal to $15.60$.

To determine

(d)

The base under given condition.

Answer to Problem 22AR

$89.02$

Explanation of Solution

Given information:

Rate is given as $82\%$ and percentage is $73$. 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 $82\%$. i.e. $R=$$82$.

Also, percentage $P=$$73$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{73}{B}=\frac{82}{100}\text{ {Put }P=73\text{ and }R=82\text{}}\\ \text{Applying cross multiplication,}\\ \Rightarrow 82B=73\times 100\\ \Rightarrow B=\frac{73\times 100}{82}\\ \Rightarrow B=89.02\end{array}$

Hence, we can say that $73$ is $82\%$ of $89.02$.

To determine

(e)

The rate under given condition.

Answer to Problem 22AR

$19.05\%$

Explanation of Solution

Given information:

Base is given as $10\frac{1}{2}$ and percentage is $2$. Need to find rate(percent).

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 base is given as $10\frac{1}{2}$. i.e. $B=$$10\frac{1}{2}$

$=10.5$.

Also, percentage $P=$$2$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{2}{10.5}=\frac{R}{100}\\ \text{Applying cross multiplication,}\\ \Rightarrow 10.5R=2\times 100\\ \Rightarrow R=\frac{2\times 100}{10.5}\\ \Rightarrow R=19.05\end{array}$

Hence, we can say that $19.05\%$ of $10\frac{1}{2}$ is $2$.

To determine

(f)

The percentage under given condition.

Answer to Problem 22AR

$45.37$

Explanation of Solution

Given information:

Rate is given as $48\%$ and base is $94.82$.

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 $48\%$ i.e. $R=$$48$

Also, base $B=$$94.82$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{P}{94.82}=\frac{48}{100}\\ \text{Applying cross multiplication,}\\ \Rightarrow \text{100}P=48\times 94.82\\ \Rightarrow P=\frac{48\times 94.82}{100}\\ \Rightarrow P=45.37\end{array}$

Hence, $48\%$ of $94.82$ is equal to $45.37$.

To determine

(g)

The percentage under given condition.

Answer to Problem 22AR

$154$

Explanation of Solution

Given information:

Rate is given as $72.4\%$ and base is $212.7$.

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 $72.4\%$ i.e. $R=$$72.4$

Also, base $B=$$212.7$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{P}{212.7}=\frac{72.4}{100}\\ \text{Applying cross multiplication,}\\ \Rightarrow \text{100}P=72.4\times 212.7\\ \Rightarrow P=\frac{72.4\times 212.7}{100}\\ \Rightarrow P=154\end{array}$

Hence, $72.4\%$ of $212.7$ is equal to $154$.

To determine

(h)

The rate under given condition.

Answer to Problem 22AR

$112.28\%$

Explanation of Solution

Given information:

Base is given as $228$ and percentage is $256$. Need to find rate(percent).

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 base is given as $228$. i.e. $B=$$228$.

Also, percentage $P=$$256$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{256}{228}=\frac{R}{100}\\ \text{Applying cross multiplication,}\\ \Rightarrow 228R=256\times 100\\ \Rightarrow R=\frac{256\times 100}{228}\\ \Rightarrow R=112.28\end{array}$

Hence, we can say that $112.28\%$ of $228$ is $256$.

To determine

(i)

The base under given condition.

Answer to Problem 22AR

$58.05$

Explanation of Solution

Given information:

Rate is given as $88\%$ and percentage is $51.08$. 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 $88\%$. i.e. $R=$$88$.

Also, percentage $P=$$51.08$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{51.08}{B}=\frac{88}{100}\text{ {Put }P=51.08\text{ and }R=88\text{}}\\ \text{Applying cross multiplication,}\\ \Rightarrow 88B=51.08\times 100\\ \Rightarrow B=\frac{51.08\times 100}{88}\\ \Rightarrow B=58.05\end{array}$

Hence, we can say that $51.08$ is $88\%$ of $58.05$.

To determine

(j)

The rate under given condition.

Answer to Problem 22AR

$132.25\%$

Explanation of Solution

Given information:

Base is given as $27.6$ and percentage is $36.5$. Need to find rate(percent).

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 base is given as $27.6$. i.e. $B=$$27.6$.

Also, percentage $P=$$36.5$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{36.5}{27.6}=\frac{R}{100}\\ \text{Applying cross multiplication,}\\ \Rightarrow 27.6R=36.5\times 100\\ \Rightarrow R=\frac{36.5\times 100}{27.6}\\ \Rightarrow R=132.25\end{array}$

Hence, we can say that $132.25\%$ of $27.6$ is $36.5$.

To determine

(k)

The percentage under given condition.

Answer to Problem 22AR

$154$

Explanation of Solution

Given information:

Rate is given as $2\frac{1}{4}\%$ and base is $150$.

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 $2\frac{1}{4}\%$ i.e. $R=$$2\frac{1}{4}=2.25$

Also, base $B=$$150$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{P}{150}=\frac{2.25}{100}\\ \text{Applying cross multiplication,}\\ \Rightarrow \text{100}P=2.25\times 150\\ \Rightarrow P=\frac{2.25\times 150}{100}\\ \Rightarrow P=3.38\end{array}$

Hence, $2\frac{1}{4}\%$ of $150$ is equal to $3.38$.

To determine

(l)

The percentage under given condition.

Answer to Problem 22AR

$21.72$

Explanation of Solution

Given information:

Rate is given as $18\%$ and base is $120.66$.

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 $18\%$ i.e. $R=$$18$

Also, base $B=$$120.66$.

Putting these value in standard proportion,

$\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{P}{120.66}=\frac{18}{100}\\ \text{Applying cross multiplication,}\\ \Rightarrow \text{100}P=18\times 120.66\\ \Rightarrow P=\frac{18\times 120.66}{100}\\ \Rightarrow P=21.72\end{array}$

Hence, $18\%$ of $120.66$ is equal to $21.72$.