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The composition of railway ticket consists of two fares i.e. per km charges and the reservation charges. Akhil travelled in a super fast train for 250 km and the expense occurred is Rs. 2400. While coming back, he took express train in which he covered a journey of 250 km and the expense occurred is Rs. 900. If the difference of rate charged per km in both trains is Rs. 5. Find the reservation charges of both the trains if they are in ratio 3: 2.

The composition of railway ticket consists of two fares i.e. per km charges and the reservation charges. Akhil travelled in a super fast train for 250 km and the expense occurred is Rs. 2400. While coming back, he took express train in which he covered a journey of 250 km and the expense occurred is Rs. 900. If the difference of rate charged per km in both trains is Rs. 5. Find the reservation charges of both the trains if they are in ratio 3: 2. Correct Answer Rs. 750, Rs. 500

Let the rater per km for superfast train and express train be x and y respectively

Let the reservation charges for superfast train and express train be a and b respectively

x - y = 5     ---- (1)

250x + a = 2400     ---- (2)

250y + b = 900     ---- (3)

Subtracting 3 from 2

250(x - y) + (a - b) = 1500

⇒ 250 × 5 + (a - b) = 1500

⇒ 1250 + (a - b) = 1500

a - b = 250     ---- (4)

a and b represent the reservation charges of both the trains so let a = 3t and b = 2t

Using equation (4)

3t - 2t = 250

t = 250

⇒ 3t = 750

⇒ 2t = 500

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