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:

Option 1: $\frac{5}{9}$

Option 2: $\frac{21}{25}$

Option 3: $1\frac{4}{5}$

Option 4: $5\frac{1}{4}$

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:

Option 1: $4:15$

Option 2: $15:4$

Option 3: $4:21$

Option 4: $21:4$

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:

Option 1: 150

Option 2: 152

Option 3: 154

Option 4: 156

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:

Option 1: $1\frac{15}{16}$

Option 2: $2\frac{15}{16}$

Option 3: $3\frac{15}{16}$

Option 4: $4\frac{15}{16}$

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 $\Delta$QBC}}{\text{Area of  $\Delta$PAC}}$ is equal to:

Option 1: $\frac{1}{2}$

Option 2: $\frac{2}{1}$

Option 3: $\frac{1}{3}$

Option 4: $\frac{2}{3}$