Question

Here is an old brainteaser by the Central Asian scholar Biruni (973−1048). If 10 dirhams (a unit of currency) earn 5 dirhams of profit in 2 months, how much profit will 8 dirhams earn in 3 months?

Answer 1

10 units earn a profit of 5 in 2 months

that means

1 unit earns a profit of 0.5 in 2 months

that means

1 unit earns a profit of 0.25 in 1 month

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8 units earn a profit 8*0.25=2 in 1 month

8 units earn a profit of 3*2=6 in 3 months