The body mass index, BMI, of a person is defined as $\displaystyle\frac{\text{mass in kg}}{(\text{height in metres})^2}$. Over two years, Jay's mass decreased by 0.8% and his height increased by 2%. Find the percentage change in Jay's BMI. Answer ... %

1. Represent the original and new mass and height using percentage multipliers.

Let Jay's original mass be $m$ kg and original height be $h$ m.

Mass decreased by $0.8\%$, so new mass
$=0.992m.$

Height increased by $2\%$, so new height
$=1.02h.$

2. Form the ratio of the new BMI to the original BMI.

Original BMI
$=\frac{m}{h^2}.$

New BMI
$=\frac{0.992m}{(1.02h)^2}.$

Hence
$\frac{\text{new BMI}}{\text{original BMI}}=\frac{\frac{0.992m}{(1.02h)^2}}{\frac{m}{h^2}}=\frac{0.992}{1.02^2}.$

3. Calculate the percentage change in BMI.

$\frac{0.992}{1.02^2}=\frac{0.992}{1.0404}=0.953479\ldots$

Percentage change
$=(0.953479\ldots-1)\times100\%=-4.6520\ldots\%.$

So Jay's BMI decreased by $4.65\%$ to 3 significant figures.