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A number is split into two parts in the ratio 5 : 6. The sum of 60% of the first part and 50% of the second part equals 84. If each part is increased by 10, what is the ratio of the sum of the original two parts to the sum of the two new parts?

1. 75 : 87
2. 73 : 87
3. 77 : 87
4. 71 : 87

Correct answer: 77 : 87

Solution

Let the two parts be 5x and 6x. Then 0.6(5x) + 0.5(6x) = 3x + 3x = 6x = 84, so x = 14. Original parts: 70 and 84; sum = 154. After adding 10 each: 80 and 94; sum = 174. Ratio = 154 : 174 = 77 : 87.

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