Question

The length and breadth of a rectangular plot are increased by $10$% and $5$%. By what percent will its area increase?

• A. $15.5$%
• B. $16.5$%
• C. $17.5$%
• D. $14.5$%

Answer 1

The correct option is A $15.5$%

Let

The length of rectangle box = ${}^{\prime }{\ell }^{\prime }$

Breadth of rectangular box = ${}^{\prime }{b}^{\prime }$

A$=$ Area $=\ell b$

Now Length is incresed by $10\%$.

$\therefore L=\ell +\frac{10}{100}\times \ell$

$L=1.1\ell$

Breadth is increased by $5\%$

$B=b+\frac{5}{100}\times b$

$\therefore B=1.05b$

$\therefore A^1=LB$

$=1.1\ell \times 1.05b$

$=A^1=1.155\ell b$

$\%$ in Area $=\frac{A^1-A}{A}\times 100$

$\therefore \frac{1.155\ell b-\ell b}{\ell b}\times 100$

$=(1.155-1)\times 100$

$=0.155\times 100$

$=15.5\%$