Four friends - Arjan, Bhuvan, Guran and Lakha were comparing the number of sheep that they owned.

It was found that Guran had ten more sheep than Lakha.

If Arjan gave one-third to Bhuvan, and Bhuvan gave a quarter of what he then held to Guran, who then passed on a fifth of his holding to Lakha, they would all have an equal number of sheep.

How many sheep did each of them possess? Give the minimal possible answer

Answer:

Arjan, Bhuvan, Guran and Lakha had 90, 50, 55 and 45 sheep respectively.

Assume that Arjan, Bhuvan, Guran and Lakha had A, B, G and L sheep respectively. As it is given that at the end each would have an equal number of sheep, comparing the final numbers from the above table.

Arjan's sheep = Bhuvan's sheep

2A/3 = A/4 + 3B/4

8A = 3A + 9B

5A = 9B

Arjan's sheep = Guran's sheep

2A/3 = A/15 + B/5 + 4G/5

2A/3 = A/15 + A/9 + 4G/5 (as B=5A/9)

30A = 3A + 5A + 36G

22A = 36G

11A = 18G

Arjan's sheep = Lakha's sheep

2A/3 = A/60 + B/20 + G/5 + L

2A/3 = A/60 + A/36 + 11A/90 + L (as B=5A/9 and G=11A/18)

2A/3 = A/6 + L

A/2 = L

A = 2L

Also, it is given that Guran had ten more sheep than Lakha.

G = L + 10

11A/18 = A/2 + 10

A/9 = 10

A = 90 sheep

Thus, Arjan had 90 sheep, Bhuvan had 5A/9 i.e. 50 sheep, Guran had 11A/18 i.e. 55 sheep and Lakha had A/2 i.e. 45 sheep.

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