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Railway fares of 1st, 2nd and 3rd classes between two stations were in the ratio of 8 : 6 : 3. The fares of 1st and 2nd class were subsequently reduced by 1/6 and 1/12 respectively. If during a year the ratio between the passengers of 1st, 2nd and 3rd classes was 9 : 12 : 26 and the total amount collected by the sale of tickets was Rs. 1088, then find the collection from the passengers of 1st class.

1Rs. 260
2Rs. 280
3Rs. 300
4Rs. 320

Answer:- 1

Explanation:-

Solution:

Let the initial fares of 1st, 2nd and 3rd class be Rs. 8x, Rs. 6x, and Rs. 3x respectively.

\begin{aligned} Revised fare of 1st class \\ = \frac{5}{6} of Rs .8 x \\ = Rs . (\frac{20 x}{3}) . \\ Revised fare of 2 nd class \\ = \frac{11}{12} of Rs .6 x \\ = Rs . (\frac{11 x}{2}) . \end{aligned}

$\eqalign{ & {\text{Revised fare of 1st class}} \cr & {\text{ = }}\frac{5}{6}{\text{of Rs}}.8x \cr & = {\text{Rs}}.\left( {\frac{{20x}}{3}} \right). \cr & {\text{Revised fare of }}2{\text{nd class}} \cr & {\text{ = }}\frac{{11}}{{12}}{\text{of Rs}}.6x \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{11x}}{2}} \right). \cr}$ Let the number of passengers of 1st, 2nd and 3rd class be 9y, 12y and 26y respectively.
Then,

\begin{aligned} = \frac{20 x}{3} \times 9 y + \frac{11 x}{2} \times 12 y + 3 x \times 26 y = 1088 \\ \Rightarrow 60 x y + 66 x y + 78 x y = 1088 \\ \Rightarrow 204 x y = 1088 \\ \Rightarrow x y = \frac{1088}{204} = \frac{16}{3} . \end{aligned}

$\eqalign{ & = \frac{{20x}}{3} \times 9y + \frac{{11x}}{2} \times 12y + 3x \times 26y = 1088 \cr & \Rightarrow 60xy + 66xy + 78xy = 1088 \cr & \Rightarrow 204xy = 1088 \cr & \Rightarrow xy = \frac{{1088}}{{204}} = \frac{{16}}{3}. \cr}$ ∴ Collection from passengers of 1st class = 60xy

\begin{aligned} = Rs . (60 \times \frac{16}{3}) \\ = Rs .320 . \end{aligned}

$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {60 \times \frac{{16}}{3}} \right) \cr & = {\text{Rs}}.320. \cr}$

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Let the number of passengers of 1st, 2nd and 3rd class be 9y, 12y and 26y respectively.
Then,

\begin{aligned} = \frac{20 x}{3} \times 9 y + \frac{11 x}{2} \times 12 y + 3 x \times 26 y = 1088 \\ \Rightarrow 60 x y + 66 x y + 78 x y = 1088 \\ \Rightarrow 204 x y = 1088 \\ \Rightarrow x y = \frac{1088}{204} = \frac{16}{3} . \end{aligned}

$\eqalign{ & = \frac{{20x}}{3} \times 9y + \frac{{11x}}{2} \times 12y + 3x \times 26y = 1088 \cr & \Rightarrow 60xy + 66xy + 78xy = 1088 \cr & \Rightarrow 204xy = 1088 \cr & \Rightarrow xy = \frac{{1088}}{{204}} = \frac{{16}}{3}. \cr}$ ∴ Collection from passengers of 1st class = 60xy

\begin{aligned} = Rs . (60 \times \frac{16}{3}) \\ = Rs .320 . \end{aligned}

$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {60 \times \frac{{16}}{3}} \right) \cr & = {\text{Rs}}.320. \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

Let the initial fares of 1st, 2nd and 3rd class be Rs. 8x, Rs. 6x, and Rs. 3x respectively.

\begin{aligned} Revised fare of 1st class \\ = \frac{5}{6} of Rs .8 x \\ = Rs . (\frac{20 x}{3}) . \\ Revised fare of 2 nd class \\ = \frac{11}{12} of Rs .6 x \\ = Rs . (\frac{11 x}{2}) . \end{aligned}

$\eqalign{ & {\text{Revised fare of 1st class}} \cr & {\text{ = }}\frac{5}{6}{\text{of Rs}}.8x \cr & = {\text{Rs}}.\left( {\frac{{20x}}{3}} \right). \cr & {\text{Revised fare of }}2{\text{nd class}} \cr & {\text{ = }}\frac{{11}}{{12}}{\text{of Rs}}.6x \cr & = {\text{Rs}}{\text{.}}\left( {\frac{{11x}}{2}} \right). \cr}$ Let the number of passengers of 1st, 2nd and 3rd class be 9y, 12y and 26y respectively.
Then,

\begin{aligned} = \frac{20 x}{3} \times 9 y + \frac{11 x}{2} \times 12 y + 3 x \times 26 y = 1088 \\ \Rightarrow 60 x y + 66 x y + 78 x y = 1088 \\ \Rightarrow 204 x y = 1088 \\ \Rightarrow x y = \frac{1088}{204} = \frac{16}{3} . \end{aligned}

$\eqalign{ & = \frac{{20x}}{3} \times 9y + \frac{{11x}}{2} \times 12y + 3x \times 26y = 1088 \cr & \Rightarrow 60xy + 66xy + 78xy = 1088 \cr & \Rightarrow 204xy = 1088 \cr & \Rightarrow xy = \frac{{1088}}{{204}} = \frac{{16}}{3}. \cr}$ ∴ Collection from passengers of 1st class = 60xy

\begin{aligned} = Rs . (60 \times \frac{16}{3}) \\ = Rs .320 . \end{aligned}

$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {60 \times \frac{{16}}{3}} \right) \cr & = {\text{Rs}}.320. \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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