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MAT Exam 2024 Paper

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Question : 44 of 150

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Eighty kilogram of store material is to be transported to a location 10 km away. Any number of couriers can be used to transport the material. The material can be packed in any number of units of 10,20 or 40 kg . Courier charges are Rs. 10 per hour. Couriers travel at the speed of

10 \mathrm{~km} / \mathrm{hr}

if they are not carrying any load, at

5 \mathrm{~km} / \mathrm{hr}

if carrying 10 kg , at

2 \mathrm{~km} / \mathrm{hr}

if carrying 20 kg and at

1 \mathrm{~km} / \mathrm{hr}

if carrying 40 kg . A courier cannot carry more than 40 kg of load. The minimum cost at which 80 kg of store material can be transported to its destination will be (given the total quantity must be sent by using one kinds of packs only, a combination of packs is not allowed)

₹ 180
₹ 160
₹ 140
₹ 120

Solution:

Concept:

For a fixed pack size, cost is: number of packs × time taken per pack × ₹10/hour, where time = distance ÷ carrying speed.

Explanation:

If packs are

10\ \mathrm{kg}

: number of packs

= 8

, time

= \frac{10}{5} = 2\ \mathrm{h}

, cost

= 8 \times 2 \times 10 = \mathrm{Rs.}\ 160

.

If packs are

20\ \mathrm{kg}

: number of packs

= 4

, time

= \frac{10}{2} = 5\ \mathrm{h}

, cost

= 4 \times 5 \times 10 = \mathrm{Rs.}\ 200

.

If packs are

40\ \mathrm{kg}

: number of packs

= 2

, time

= \frac{10}{1} = 10\ \mathrm{h}

, cost

= 2 \times 10 \times 10 = \mathrm{Rs.}\ 200

.

Minimum cost is Rs. 160.

Answer:

Rs. 160, i.e., Option B.

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