1. If 75% of \(A\) equals 40% of \(B\), then the ratio \(A:B\) is –?

2. If \(\frac{2}{3}\) of A = 75% of B = 0.6 of C, then find the ratio A : B : C.

3. In triangle \( \triangle ABC \), AD is a median. Point E divides AD in the ratio 1:2. The extended line BE intersects AC at point F. If \( AC = 10 \) cm, find the length of \( AF \).

(a) 5 cm (b) 4 cm (c) 2 cm (d) None of the above

4. If 50% of A = 60% of B = \(\frac{4}{5}\) of C, then find the ratio A : B : C.

5. In a partnership business, the capital ratio of Sameer, Idrish, and Anthony is \(\frac{1}{6} : \frac{1}{5} : \frac{1}{4}\). If the total profit at the end of the year is ₹3,700, find Anthony's share of the profit.

6. 75% of A = 50% of B; Find the ratio A : B.

7. A right circular cylinder has a height-to-base-radius ratio of 3:1. If the volume of the cylinder is \(1029\pi\) cubic cm, find the total surface area of the cylinder.

8. \[ \frac{1}{(x - 1)(x - 2)} + \frac{1}{(x - 2)(x - 3)} + \frac{1}{(x - 3)(x - 4)} = \frac{1}{6} \] This is a mathematical equation involving rational expressions. Here's the English translation of the statement: **"The sum of the following three fractions equals one-sixth:"** - The first fraction is: one divided by \((x - 1)(x - 2)\) - The second fraction is: one divided by \((x - 2)(x - 3)\) - The third fraction is: one divided by \((x - 3)(x - 4)\) And their total is equal to \(\frac{1}{6}\).

9. The ratio of the capital of A, B, and C is \(\frac{1}{6}:\frac{1}{5}:\frac{1}{4}\). If C's profit at the end of the year is ₹1500, find the total profit.

10. Find the compound ratio of \(\cfrac{a}{b} : c\), \(\cfrac{b}{c} : a\), and \(\cfrac{c}{a} : b\).

11. Find the compound ratio of the reciprocals of the ratios \(\displaystyle x^2:\cfrac{yz}{x},\quad y^2:\cfrac{zx}{y},\quad z^2:\cfrac{yx}{z}\).

12. If \(a : b = 3 : 4\) and \(x : y = 5 : 7\), then find the value of the ratio \((3ax - by) : (4by - 7ax)\).

13. If \(a : b = 3 : 2\) and \(b : c = 3 : 2\), then find the value of the ratio \((a + b) : (b + c)\).

14. In the right-angled triangle \(ABC\), where \(\angle B = 90^\circ\), point \(D\) lies on \(AB\) such that the ratio \(AB : BC : BD = \sqrt{3} : 1 : 1\). Find the measure of \(\angle ACD\).

15. In the cyclic quadrilateral ABCD: \(\angle A = 4x^\circ\), \(\angle B = 7x^\circ\), \(\angle C = 5y^\circ\), and \(\angle D = y^\circ\) Find the value of the ratio \(x : y\).

16. If \(xy = 5 : 1\), find the value of the ratio \(x - y^2 : x^2 + y^2\).

(a) 25:1 (b) 12:13 (c) 12:25 (d) None of the above