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Algebra Level 3

Two friends were traveling on their horses, they reached a lake side. They decided to stop and eat their lunch, while they were preparing for lunch an other rider came and asked permission to have lunch with them, because he was carrying nothing with him. They let him share their lunch. 1st rider had 5 Indian breads and 2nd had 3 Indian breads with him, they collected the breads at one place and started eating lunch, each of them ate an equal amount of bread. After the lunch, the 3rd rider gave them 10 gold coins and said goodbye.

What is the justified share of 2nd rider who shared 3 breads in the lunch?

3 2 1.25 2.5

6 solutions

Utkarsh Goel
Jun 28, 2014

If all of them ate equal no. of breads, the third rider had (8/3) breads. And since he gave 10 coins, each bread is worth (30/8) coins. Now the rider with 3 breads initially, also ate (8/3) breads. This means he gave away (1/3) bread, which is worth (10/8) coins or 1.25 coins. Hence, the answer is 1.25

I do not agree. The two riders got 10 gold coins. This means they have to spilt them ⅝ and ⅜ which makes the justified share of the second rider 3.75 goldcoins.

Mark Macqueen - 6 years, 11 months ago

Also, look at it this way... Since each rider ate 8/3=2.67 breads, first rider gave away 2.33 breads while the second one gave only 0.33 bread. Now split the 10 coins according to what they gave. Hence, they split it (2.33/2.67) and (0.33/2.67), getting shares of 8.75 and 1.25 coins respectively.

utkarsh goel - 6 years, 11 months ago

But the fact that 'they collected the breads at one place' suggests that each rider got 8/3 breads, and each of these three portions were 5/8 from the first rider, and 3/8 from the second rider, which would mean that the second rider didn't simply give away 1/3 of a bread, and his share would be 3.75 coins.

Naushad Talati - 6 years, 11 months ago

@Naushad Talati – The second rider ate 8/3 of his own bread, leaving 1/3, which has given to the third rider. The first rider ate 8/3 of his own bread, leaving 7/3 which was given to the third rider. Therefore, the third rider owes 7 times as much to the first rider as he does to the second, and thus owes 1.25, (10/8) to the second rider.

Nicolas Bryenton - 6 years, 10 months ago

This is correct - there should be no consideration of who ate what, as they all ate the same, thus 3/8 * 10 coins is the correct answer

Alistair Fleming - 6 years, 10 months ago

I did not understood why is each bread worth 30/8 coins.? Pls elaborate.

Parag Zode - 6 years, 11 months ago

It is simple unitary method.. If 8/3 breads are worth 10 coins.. 1 bread is worth 10/(8/3)=30/8

utkarsh goel - 6 years, 11 months ago

Each bread is worth 10 divided by 8/3 ... which is 30/3

lekshmanan natarajan - 6 years, 11 months ago

Typing mistake ... which is 30/8

lekshmanan natarajan - 6 years, 11 months ago

If each great is worth 30/8, then the eight breads must be worth 240/3, which is 80 gold coins for the lot. But the third rider gave them only 10 gold coins. I presume the worth of one bread is 10/8.

Mark Macqueen - 6 years, 11 months ago

@Mark Macqueen – And i think you have made some error. If each bread is worth 30/8 coins, 8 breads are worth 30 coins. And since the third rider had a third of the total breads, he gave them 30/3=10 coins (justifying the solution)

utkarsh goel - 6 years, 11 months ago

@Mark Macqueen – The 2 riders did not give all the 8 breads to the third rider. They themselves had 8/3 breads each. So the third rider gave them coins for his share only!

utkarsh goel - 6 years, 11 months ago

I disagree, the answer is approx. 3 coins. Here there were 8 breads total, and 10 coins given, so each bread is 10/8 value.Now for his 3 breads, the 2nd rider deserves 10/8 * 3 coins and the 1st rider gets 10/8 * 5 coins. So the 2nd rider gets 30/8=approx. 3 coins....its logical...

Einstein The second - 6 years, 11 months ago

oh.. thanks!

Parag Zode - 6 years, 11 months ago

a very good answer with utmost clarity

andem bhavani - 6 years, 11 months ago

good solution!

Rajat Nair - 6 years, 11 months ago

answer has to be 3.75 because coins has to be distributed among both riders depending on the rayio of bread they shared...

victor hill - 6 years, 10 months ago

if the 10 gold coins is split into 5/8 and 3/8. the second rider will be having a gain of 2.5 gold coins. therefore the answer turns out to be 1.25

vinayak p - 6 years, 10 months ago

Joram Otero
Jul 1, 2014

Each of them ate 8/3 breads. If the 2nd rider shared 3 breads that means he only gave 3 - (8/3) bread to the 3rd rider which is 1/3 bread only. Then the percentage of the 2nd rider's donation to the 3rd rider is (1/3)/(8/3) and that would be 1/8 only. Therefore he can only get 1/8 of the 10 coins and that is 1.25.

Good justified answer

Sadanand Naik - 6 years, 11 months ago

thanks man

joram otero - 6 years, 11 months ago

Vinayak P
Aug 3, 2014

if the 10 gold coins is split into 5/8 and 3/8. the second rider will be having a gain of 2.5 gold coins. therefore the answer turns out to be 1.25

Vaibhav Shete
Jul 7, 2014

The third rider ate 8/3 breads and gave 10 coins.

So price of one bread is 10/(8/3) coins.

For the sake of simplicity , lets assume 2nd rider bought a bread from 1st rider before starting, giving 10/(8/3) coins.

So now both riders have 4 breads each.

Now while eating, 3rd rider took equal amount of bread from both. So they would divide his money equally. 5 coins each.

Therefore, 2nd rider gets 5-(10/(8/3)) coins (considering the previous transaction between 1st and second rider done for simplicity). Which equals 1.25.

Sam Cheung
Jul 1, 2014

The first rider contributed 5/8ths of the bread and the second 3/8ths. Each then eat a third of the bread. This means that the contribution from each rider to the third is as follows:

1st rider : 5/8 - 1/3 = 7/24

2nd rider : 3/8 - 1/3 = 1/24

Which means the 10 gold should be divided into eighths, with the second rider getting 1/8.

10/8 = 1.25

Sree Vidya
Jun 29, 2014

each person ate 2.66 part of bread 2.66 part of bread cost 10 coins 0.33 from 2nd traveler and 2.33 from 1st traveler that gives (0.334/2.66)*10=1.25 :)

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