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A transport agency has 5 carriers, each of capacity 15 tonnes. The car

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Bunuel
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A transport agency has 5 carriers, each of capacity 15 tonnes. The car [#permalink] New post   08 Dec 2020, 05:30
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A transport agency has 5 carriers, each of capacity 15 tonnes. The carriers are scheduled such that the first carrier makes a trip every day, the second carrier makes a trip every second. The third makes a trip every third day and so on. Find the maximum number of times in a year that it is possible to dispatch a total shipment of 75 tonnes in a single day. The operation starts on the 7th January 2010 and continue till the end of the year (31st December 2010) without any holiday.

A. 8

B. 7

C. 6

D. 5

E. 4
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mcmoorthy
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A transport agency has 5 carriers, each of capacity 15 tonnes. The car [#permalink] New post   08 Dec 2020, 06:43
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Each truck of the 5 trucks has a capacity of 15 tonnes and we need to ship 75 tonnes.

Truck 1 has a frequency of 1 trip per day , truck 2 every 2nd day, truck 3 every 3rd day, truck 4 every 4th day, and truck 5 every 5th day.

We need all the trucks to run at the same day so that we can ship 15*5 tonnes making 75 tonnes.

So lets calculate the LCM for 1,2,3,4,5 which is 60. Every 60 days all the trucks will carry load and the total shipment carried that day will be 75 tonnes.

In a year there are 365 days and since we start at Jan 7 we are looking at less than 360 days.

Total trips is less than 360/60 which is less than 6 which makes the maximum number as 5.

Ans D

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Re: A transport agency has 5 carriers, each of capacity 15 tonnes. The car [#permalink] New post   15 Dec 2020, 07:03
Bunuel, chetansharma, yashikaaggarwal, could either of you post the OE to this question or better still could you post your approach on how to tackle these kinds of questions ?
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Re: A transport agency has 5 carriers, each of capacity 15 tonnes. The car [#permalink] New post   15 Dec 2020, 11:51
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kntombat wrote:
Bunuel, chetansharma, yashikaaggarwal, could either of you post the OE to this question or better still could you post your approach on how to tackle these kinds of questions ?

The above-said method is good.
We know only 5 trucks can dispatch 75 tonnes of goods.
so if on 7th Jan the trucks are loaded with 75 tonnes
so the next time they will be loaded with 75 tonnes all together = LCM of 1,2,3,4, and 5 = 60 (the trucks meet on every 60th-day interval)
since days are to be count = 358 (365 - 7 from Jan)
so the trucks will be loaded 5 more times
going a total of 6 times in the given year.
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Re: A transport agency has 5 carriers, each of capacity 15 tonnes. The car [#permalink] New post   15 Dec 2020, 17:42
yashikaaggarwal wrote:
The above-said method is good.
We know only 5 trucks can dispatch 75 tonnes of goods.
so if on 7th Jan the trucks are loaded with 75 tonnes
so the next time they will be loaded with 75 tonnes all together = LCM of 1,2,3,4, and 5 = 60 (the trucks meet on every 60th-day interval)
since days are to be count = 358 (365 - 7 from Jan)
so the trucks will be loaded 5 more times
going a total of 6 times in the given year.


Hi,

Quote:
so if on 7th Jan the trucks are loaded with 75 tonnes
- The question states that the service starts on 7th January 2010, but did not mention that trucks are loaded with 75 tonnes on the day 1.

Shouldn't we consider that 7th january truck 1 is dispatched and 5th truck is dispatched on 11th January rather than considering all trucks were dispatched on 7th January ? I calculated this way and got answer as '5' , but official answer is 6.
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Re: A transport agency has 5 carriers, each of capacity 15 tonnes. The car [#permalink] New post   07 Jan 2021, 09:57
The LCM for 1, 2, 3, 4, and 5 = 60

365 - 7 = 358 days

1(1), 61(2), 121(3), 181(4), 241(5), 301(6), >361<
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Re: A transport agency has 5 carriers, each of capacity 15 tonnes. The car [#permalink] New post   07 Jan 2021, 19:50
akadiyan wrote:
yashikaaggarwal wrote:
The above-said method is good.
We know only 5 trucks can dispatch 75 tonnes of goods.
so if on 7th Jan the trucks are loaded with 75 tonnes
so the next time they will be loaded with 75 tonnes all together = LCM of 1,2,3,4, and 5 = 60 (the trucks meet on every 60th-day interval)
since days are to be count = 358 (365 - 7 from Jan)
so the trucks will be loaded 5 more times
going a total of 6 times in the given year.


Hi,

Quote:
so if on 7th Jan the trucks are loaded with 75 tonnes
- The question states that the service starts on 7th January 2010, but did not mention that trucks are loaded with 75 tonnes on the day 1.

Shouldn't we consider that 7th january truck 1 is dispatched and 5th truck is dispatched on 11th January rather than considering all trucks were dispatched on 7th January ? I calculated this way and got answer as '5' , but official answer is 6.


akadiyan
I made the same mistake. And yes it doesn't really say that all the trucks were dispatched on 7th jan, but it is also not mentioned that only the first truck was dispatched on the first day like we (you and I, both) thought. And the question asks us to find the maximum "Possible" shipment of 75 tonnes. And 6 shipments are indeed possible if you consider that all of them were shipped on the first day. "Possible" is the word that makes this question difficult.

Hope this helps!
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A transport agency has 5 carriers, each of capacity 15 tonnes. The car [#permalink] New post   19 Aug 2021, 18:21
A transport agency has 5 carriers, each of capacity 15 tonnes. The carriers are scheduled such that the first carrier makes a trip every day, the second carrier makes a trip every second. The third makes a trip every third day and so on. Find the maximum number of times in a year that it is possible to dispatch a total shipment of 75 tonnes in a single day. The operation starts on the 7th January 2010 and continue till the end of the year (31st December 2010) without any holiday.

What from this stem implies that all five will carriers will all start on the first day? The bolded sentence seems to imply this is not the case...
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A transport agency has 5 carriers, each of capacity 15 tonnes. The car [#permalink]
19 Aug 2021, 18:21
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