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Two numbers are increased at a rate of 20% and 30% per annum. If the numbers are in a ratio 8 : 9, find the ratio of the numbers after 2 years.

Two numbers are increased at a rate of 20% and 30% per annum. If the numbers are in a ratio 8 : 9, find the ratio of the numbers after 2 years. Correct Answer 128 : 169

Let the numbers be 80 and 90, respectively. The numbers after 1 year = 80 + 20% of 80, 90 + 30% of 90 = 80 + 16, 90 + 27 = 96, 117 The numbers after 2 years = 96 + 20% of 96, 117 + 30% of 117 = 96 + 19.2, 117 + 35.1 = 115.2, 152.1 The ratio of the numbers after 2 years = 1152 : 1521 = 128 : 169

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