Question : In $\triangle$ABC, D and E are two points on the sides AB and AC, respectively, so that DE $\parallel$ BC and $\frac{AD}{BD}=\frac{2}{3}$. Then $\frac{\text{Area of trapezium DECB}}{\text{Area of $\triangle$ABC}}$ is equal to:

Question : In $\triangle ABC$, $D$ and $E$ are the points of sides $AB$ and $BC$ respectively such that $DE \parallel AC$ and $AD : DB = 3 : 2$. The ratio of the area of trapezium $ACED$ to that of $\triangle DBE$ is:

Question : The sides of similar triangle $\triangle ABC$ and $\triangle DEF$ are in the ratio of $\frac{\sqrt{3}}{\sqrt{5}}$. If the area of $\triangle ABC$ is $90 \text{ cm}^2$, then the area of $\triangle DFF\left(\right.$ in $\left.\text{cm}^2\right)$ is:

Question : A can finish a work in 7 days. B can finish the same work in 9 days. The number of days required to finish the same work by both of them together is:

Question : ABCD is a square. Draw a triangle QBC on side BC considering BC as a base and draw a triangle PAC on AC as its base such that $\Delta$QBC$\sim\Delta$PAC. Then, $\frac{\text{Area of $\Delta