A family of 4 members travelling in a $3^{r d}$ tier coach of a train and a family of 3 members travelling in a 2-tier coach of the same train pay Rs.5100 in total. The total fare would have been Rs.300 more if the first family has 1 member less while the second had 1 member more. What will be the fare for a couple for the same journey in a 2 tier coach?

900

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1200

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1800

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1400

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Solution

The correct option is C
1800

Let fare for a 3 tier coach be Rs. x and fare for a 2-tier coach be Rs. y

For first family, total fare = 4x

For second family, total fare = 3y

According to the problem, 4x + 3y = 5100 ....(i)

In second family, total fare

3x + 4y = 5100 + 300

$\Rightarrow$ 3x + 4y = 5400….(ii)

On solving (i) and (ii), we get

y = Rs. 900

The fare of a couple in 2 tier coach = 2y = 2 $\times$ 900 = Rs. 1800.

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