Question

Are the following statements true? $7.5\mathrm{litre}:15\mathrm{litre}=5\mathrm{kg}:10\mathrm{kg}$

• A. True
• B. False

Answer 1

The correct option is A True

$\begin{array}{rcl}\mathrm{Ratio}\mathrm{of}7.5\mathrm{litre}\mathrm{to}15\mathrm{litre}& =& \frac{7.5}{15}\\ & =& \frac{75}{150}\\ & & \mathrm{Dividing}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{by}75\\ & =& \frac{1}{2}\\ & =& 1:2\end{array}$

$\begin{array}{rcl}\mathrm{Ratio}\mathrm{of}5\mathrm{kg}\mathrm{to}10\mathrm{kg}& =& \frac{5}{10}\\ & & \mathrm{Dividing}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{by}5\\ & =& \frac{1}{2}\\ & =& 1:2\end{array}$

Since, $7.5\mathrm{litre}:15\mathrm{litre}=5\mathrm{kg}:10\mathrm{kg}$

Hence, $7.5\mathrm{litre}:15\mathrm{litre}=5\mathrm{kg}:10\mathrm{kg}$ are in proportion. Given statement is true.