Question

In a survey ratio of people who liked Algebra and geometry in the ratio is 9:8. If 25% like both, 80 liked none of these and 20% like Algebra only. Find the total number of people participated in survey​

Answer 1

Let the number of people who liked Algebra be 9x and the number of people who liked Geometry be 8x. Then, we know that:

- The total number of people who participated in the survey is 9x + 8x + 80 (the sum of those who liked Algebra, those who liked Geometry, and those who liked neither).

- 25% of the total number of people participated in the survey like both Algebra and Geometry. Therefore, the number of people who like both is 0.25(9x) + 0.25(8x) = 4.25x.

- 20% of the total number of people participated in the survey like Algebra only. Therefore, the number of people who like Algebra only is 0.20(9x) = 1.8x.

We can now set up two equations based on the information above and solve for x:

9x + 8x + 80 = 4.25x + 1.8x + 80

17.8x = 4.25x + 1.8x

x = 5.00

So the number of people who liked Algebra is 9x = 45, and the number who liked Geometry is 8x = 40. The number of people who liked both is 4.25x = 21.25, and the number who liked neither is 80.

Therefore, the total number of people who participated in the survey is:

9x + 8x + 80 = 17x + 80 = 17(5) + 80 = 155

So the total number of people who participated in the survey is 155.