Bidyut Guha Thakurta and Amitava Mitra Solutions for Exercise 8: SECOND SUMMATIVE TEST

In a joint business the capital of Suvendu and Nausat are $₹6000$ and $₹4800$. After $3$ months Suvendu withdraws $₹4500$ and Nasaut withdraws $₹3200$. If the profit at the end of the year is $₹6700$, then how much profit each of them will get.

Gautam, Sunil and Saugat start a joint business with $₹6000,₹8000$ and $₹9000$. After some months Gautam invests $₹3000$ more in the business. At the end of the year the total profit is $₹3000$ and Saugat gets $₹1080$ as profit. After how many months Gautam gave $₹3000$?

If $x^2\propto yz,y^2\propto zx$ and $z^2\propto xy$ then, find the relation between the constants of variation.

Solve for $x$: $\frac{1}{x-a-b}=\frac{1}{x}-\frac{1}{a}-\frac{1}{b}$

Prove that, in a right-angled triangle if a perpendicular is drawn from the right angle to the hypotenuse then the two triangles so formed are similar to the original triangle, and also they are similar to each other.

Prove that the tangent at any point to a circle and the radius through the point of contact are perpendicular to each other.

Draw a triangle whose two sides are $7 \mathrm{cm}$ and $9 \mathrm{cm}$ and the included angle is $90°$. Draw the incircle of the triangle.

The height of a right circular cone is $21 \mathrm{cm}$ and volume is $4312 {\mathrm{cm}}^3$. If the radius of the base is $r$ and slant height $l$, then find the value of $r^2+l^2$.