Rani bought more apples than oranges. She sells apples at $₹23$ per piece and makes $15\%$ profit. She sells oranges at $₹10$ per piece and makes $25\%$ profit. If she gets $₹653$ after selling all the apples and oranges, find her profit percentage.

In the figure below, $\mathrm{AB}=\mathrm{AC}=\mathrm{CD}$. If $\angle \mathrm{ADB}=20°$, what is the value of $\angle \mathrm{BAD}?$

$∆\mathrm{ABC}$ and $\mathrm{\Delta XYZ}$ are equilateral triangles of $54 \mathrm{cm}$ sides. All smaller triangles like $∆\mathrm{ANM},∆\mathrm{OCP},\mathrm{\Delta QPX}$ etc. are also equilateral triangles. Find the area of the shape MNOPQRM.

A person standing on the ground at point $\mathrm{A}$ saw an object at point $\mathrm{B}$ on the ground at a distance of $600 \mathrm{m}$. The object started flying towards him at an angle of $30°$ with the ground. The person saw the object for the second time at point $\mathrm{C}$ flying at $30°$angle with him. At point $\mathrm{C}$, the object changed direction and continued flying upwards. The person saw the object for the third time when the object was directly above him. The object was flying at a constant speed of $10 \mathrm{km}/\mathrm{h}$.

Find the angle at which the object was flying after the person saw it for the second time. You may use additional statement(s) if required.

Statement I: After changing direction, the object took $3$ more minutes than it had taken before.

Statement II: After changing direction, the object travelled an additional $200\sqrt{3} \mathrm{m}$.