Chapter 15.1, Problem 17PSC

To determine

To Find: The solution of the given expression.

Answer to Problem 17PSC

  $x=z+44\%z$

Explanation of Solution

Given:

  $\begin{array}{l}x\text{ exceeds }y\text{by }20\%\\ y\text{ exceeds }z\text{by}20\%\end{array}$

Formula Used:

  $\left(x+a\right)\left(x+b\right)=x^2+\left(a+b\right)x+ab$

  $a\%b=\frac{a}{b}\times 100$

Calculation:

  $\begin{array}{l}x\text{ exceeds }y\text{by }20\%\\ y\text{ exceeds }z\text{by}20\%\\ \text{From above}\\ x=y+20\%y\\ \text{⇒}x=y+\frac{20y}{100}\\ \text{⇒}x=\frac{100y+20y}{100}\\ \text{⇒}100x=120y\\ \text{⇒}y=\frac{100}{120}x\\ y=z+20\%z\\ \text{On putting }y\text{in above expression one will get}\\ \text{⇒}\frac{100}{120}x=z+\frac{20z}{100}\\ \text{⇒}\frac{100}{120}x=\frac{100z+20z}{100}\\ \text{⇒}\frac{100}{120}x=\frac{120z}{100}\\ \text{⇒}x=\frac{120\times 120}{100\times 100}z\\ \text{⇒}x=\frac{14400}{10000}z\\ \text{⇒}x=\frac{144}{100}z\\ \text{⇒}x=\frac{100+44}{100}z\\ \text{⇒}x=z+\frac{44}{100}z\\ \text{⇒}x=z+44\%z\end{array}$

Conclusion:

Thus, the $x\text{ will exceeds }z\text{ by 44\%}$