$$\eqalign{ & {\text{Second}}:{\text{Third}} \cr & = {\text{9}}:{\text{16}} \cr & {\text{Third}}:{\text{first}} \cr & = {\text{4}}:{\text{1}} \cr & {\text{ = 16}}:{\text{4}}{\text{}} \cr & \refore {\text{Second}}:{\text{Third}}:{\text{first}} \cr & = {\text{9}}:{\text{16}}:{\text{4}}{\text{}} \cr & {\text{Second number}} \cr & = \left( {{\text{116}} \times \frac{{\text{9}}}{{{\text{29}}}}} \right) \cr & = {\text{36}} \cr} $$

Let initial fares of 1st, 2nd and 3rd class be Rs. 8x, Rs. 6x, and Rs. 3x respectively
$$\eqalign{ & {\text{Revised fare of 1st class}} \cr & {\text{ = }}\frac{5}{6}{\text{of Rs}}.8x \cr & = {\text{Rs}}.\left( {\frac{{20x}}{3}} \right) \cr & {\text{Revised fare of }}2{\text{nd class}} \cr & {\text{ = }}\frac{{11}}{{12}}{\text{of Rs}}.6x \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{11x}}{2}} \right) \cr} $$
Let number of passengers of 1st, 2nd and 3rd class be 9y, 12y and 26y respectively
Then,
$$\eqalign{ & = \frac{{20x}}{3} \times 9y + \frac{{11x}}{2} \times 12y + 3x \times 26y = 1088 \cr & \Rightarrow 60xy + 66xy + 78xy = 1088 \cr & \Rightarrow 204xy = 1088 \cr & \Rightarrow xy = \frac{{1088}}{{204}} = \frac{{16}}{3} \cr} $$
∴ Collection from passengers of 1st class = 60xy
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {60 \times \frac{{16}}{3}} \right) \cr & = {\text{Rs}}.320 \cr} $$

Let numbers are = 3x and 5x
∴ According to question,
$$\eqalign{ & \Rightarrow \frac{{3x + 6}}{{5x + 6}} = \frac{2}{3} \cr & \Rightarrow 9x + 18 = 10x + 12 \cr & \Rightarrow x = 6 \cr & {\text{So, numbers are }} \cr & 3x = 3 \times 6 = 18 \cr & 5x = 5 \times 6 = 30 \cr} $$

a   :   b   ::   c   :   d
    a × d = b × c
So, go through options
(A). 9 × 16 = 12 × 12 (right)
(B). 13 × 4 = 11 × 5 (wrong)
(C). 30 × 24 = 45 × 13 (wrong)
(D). 3 × 5 = 5 × 2 (wrong)
So answer is 12 : 9 :: 16 : 12

h α t²
⇒ h = kt² for some constant k
⇒ 64 = k × 2² = 4k
⇒ k = 16.
Let required height be x cm.
Then,
= x = 16 × 6² = (16 × 36) cm = 576 cm.

Given,
X : Y = 3 : 2
Y : Z = 3 : 2
Equal value of Y in both equation
X : Y = 3 : 2 (multiply with 3) and
Y : Z = 3 : 2 (multiply with 2)
i.e. X : Y = 9 : 6 and
Y : Z = 6 : 4
∴ X : Y : Z = 9 : 6 : 4

Total Run scored by A, B and C = 342
Run Scored by A = $$\frac{9}{19} \times 342 = 162$$
Run Scored by B = $$\frac{6}{19} \times 342 = 108$$
Run Scored by C = $$\frac{4}{19} \times 342 = 72$$

Sum of opposite angles in cyclic quadrilateral is 180°
∠A + ∠C = 180°
⇒ x + 4x = 180°
∴ x = 36°
Now ∠B = 3x = 3 × 36° = 108°
∠D = 180 - ∠B = 180 - 108 = 72°

$$\eqalign{ & {\text{Seema's share}} \cr & = {\text{Rs}}{\text{.}}\left( {25000 \times \frac{3}{5}} \right) \cr & = {\text{Rs}}.15000. \cr & {\text{Meena's share}} \cr & = {\text{Rs}}{\text{.}}\left( {25000 \times \frac{2}{5}} \right) \cr & = {\text{Rs}}.10000. \cr} $$
∴ Required ration
= (15000 + 5000) : (10000 + 5000)
= 4 : 3

$$\frac{{3x + 5}}{{5x - 2}} = \frac{2}{3}$$
⇒ Cross multiply equation
$$\eqalign{ & 9x + 15 = 10x - 4 \cr & x = 19 \cr} $$