In a city, there are three types of city buses – Ordinary, Metro and Luxury. The price of the ticket for each bus depends on the distance for which a passenger travels. For travelling a distance which is at most 4 km, the price of the ticket for the three types of buses are ₹20, ₹30 and ₹60 respectively. For each additional km or part thereof, the price of the ticket for the three type of buses increases by ₹8, ₹10 and ₹20 respectively. Further, there is a monthly pass – enabling unlimited travel in a month – available for each of the three types of buses, priced at ₹1000, ₹2200 and ₹6300 respectively. Any pass is valid only in the type of bus for which it is meant. Any passenger will try to minimize the total amount that he/she spends in each month on bus travel, i.e., on tickets or bus pass, considering the distance of his/her travel during the month and the cost of the monthly pass.Question No. 5DIRECTIONS for questions 4 and 5: Select the correct alternative from the given choices.Hiren, Lal and Krish travel exactly once every day by Ordinary bus, Metro bus and Luxury bus, respectively. Hiren, Lal and Krish did not buy a monthly pass for May 2023. If h, l and k represent the maximum distance that they could have travelled in a day, which of the following statements is true? h < k < l h < l < k k < h < l l < h < k
Question
In a city, there are three types of city buses – Ordinary, Metro and Luxury. The price of the ticket for each bus depends on the distance for which a passenger travels. For travelling a distance which is at most 4 km, the price of the ticket for the three types of buses are ₹20, ₹30 and ₹60 respectively. For each additional km or part thereof, the price of the ticket for the three type of buses increases by ₹8, ₹10 and ₹20 respectively. Further, there is a monthly pass – enabling unlimited travel in a month – available for each of the three types of buses, priced at ₹1000, ₹2200 and ₹6300 respectively. Any pass is valid only in the type of bus for which it is meant. Any passenger will try to minimize the total amount that he/she spends in each month on bus travel, i.e., on tickets or bus pass, considering the distance of his/her travel during the month and the cost of the monthly pass.Question No. 5DIRECTIONS for questions 4 and 5: Select the correct alternative from the given choices.Hiren, Lal and Krish travel exactly once every day by Ordinary bus, Metro bus and Luxury bus, respectively. Hiren, Lal and Krish did not buy a monthly pass for May 2023. If h, l and k represent the maximum distance that they could have travelled in a day, which of the following statements is true? h < k < l h < l < k k < h < l l < h < k
Solution
To answer this question, we need to calculate the maximum distance that Hiren, Lal, and Krish could have travelled in a day by Ordinary bus, Metro bus, and Luxury bus respectively without the cost exceeding the price of a monthly pass.
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For Hiren who travels by Ordinary bus: The price of the ticket for the first 4 km is ₹20 and for each additional km, the price increases by ₹8. If Hiren did not buy a monthly pass for ₹1000, the maximum distance he could have travelled in a day is when the cost equals ₹1000.
20 + 8(h - 4) = 1000 8h - 32 = 980 8h = 1012 h = 126.5 km
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For Lal who travels by Metro bus: The price of the ticket for the first 4 km is ₹30 and for each additional km, the price increases by ₹10. If Lal did not buy a monthly pass for ₹2200, the maximum distance he could have travelled in a day is when the cost equals ₹2200.
30 + 10(l - 4) = 2200 10l - 40 = 2170 10l = 2210 l = 221 km
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For Krish who travels by Luxury bus: The price of the ticket for the first 4 km is ₹60 and for each additional km, the price increases by ₹20. If Krish did not buy a monthly pass for ₹6300, the maximum distance he could have travelled in a day is when the cost equals ₹6300.
60 + 20(k - 4) = 6300 20k - 80 = 6240 20k = 6320 k = 316 km
So, the correct order of the maximum distance that they could have travelled in a day is h < k < l or Hiren < Krish < Lal.
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