Question
A number is divided into two parts in the ratio of 5 : 6
respectively. The sum of 60 percent of first part and 50 percent of second part is 84. If both parts are increased by 10, then what will be the respective ratio between the sum of old numbers and new numbers?Solution
Let the first part be 5x and the second part be 6x. So, 60% of 5x + 50% of 6x = 84 => [(6 /100) × 5x] + [(50/100) × 6x] = 84 => 3x + 3x = 84 => x = 14 First part = 5x = 5 × 14 = 70 Second part = 6x = 6 × 14 = 84 The old umber will be 70 + 84 = 154 According to question, First part = 5x + 10 = 70 + 10 = 80 Second part = 6x + 10 = 84 + 10 = 94 ∴ The new number obtained is 174 The ratio of the old number to the new number = 154/174 = 77/87
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