Question

Wayne wants to use Nitrogen, Potassium, and Phosphorus in his field as fertilizers. When any of them is mixed in the field, their quantity reduces by 1 kg every day due to chemical reactions. He mixed Nitrogen, Potassium, and Phosphorus on 7th November, 9th November, and 15th November, respectively. He spent equal amounts on buying each of the three. What should be the ratio of prices of Nitrogen, Potassium, and Phosphorus, so that there is an equal quantity of each of them in the field on 16th November, and that quantity is 11 kg?

Answer 1

Given: Quantities of each of Nitrogen, Potassium and Phosphorus in the field on 16th November are 11 kg.

Concept used: If equal amounts are spent on buying the components, the ratio of their prices will be inverse of ratios of their quantities.

Calculation: Nitrogen was mixed on 7th November.

Quantity of Nitrogen when it was mixed = 11 + (16 – 7) = 20 kg

Potassium was mixed on 9th November.

Quantity of Potassium when it was mixed = 11 + (16 – 9) = 18 kg

Phosphorus was mixed on 15th November.

Quantity of Phosphorus when it was mixed = 11 + (16 – 15) = 12 kg

Expenditure = quantity bought × Price per unit

⇒ Ratio of their prices = (1/20):(1/18):(1/12) = 9:10:15

∴ The required ratio is 9 ∶ 10 ∶ 15.