Two numbers are in the ratio 8:5. If eleven is subtracted from each of them, the ratio becomes 7:3. What is the product of the numbers?
640
Let the two numbers be 8x and 5x, since they are in the ratio 8:5.
According to the condition given, when 11 is subtracted from each number, the new ratio becomes 7:3, so (8x-11)/(5x-11) = 7/3.
Cross-multiplying: 3(8x-11) = 7(5x-11), which gives 24x - 33 = 35x - 77.
Solving this: 77 - 33 = 35x - 24x, so 44 = 11x, giving x = 4.
Therefore, the two numbers are 8×4 = 32 and 5×4 = 20.
Their product is 32 × 20 = 640.
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