In a train, the ratio of the number of males to the number of females is 5:6. At a train station, 8 males got off the train. The ratio of the number of males to females is now 3:4. Find the number of people in the train now.
m/f = 5/6
(m-8)/f = 3/4
6m = 5f
4m-32 = 3f
Now use your favorite method to solve for m and f, and then the total is (m-8)+f
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Let's assume the initial number of males is 5x and the initial number of females is 6x.
After 8 males got off the train, the number of males is now 5x - 8.
According to the given information, the ratio of the number of males to females is now 3:4. Therefore, we can set up the following equation:
(5x - 8) / (6x) = 3/4
Cross-multiplying the equation, we get:
4(5x - 8) = 3(6x)
20x - 32 = 18x
Subtracting 18x from both sides, we get:
2x - 32 = 0
Adding 32 to both sides, we get:
2x = 32
Dividing both sides by 2, we get:
x = 16
Now we can find the initial number of males and females:
Number of males = 5x = 5 * 16 = 80
Number of females = 6x = 6 * 16 = 96
Therefore, the initial number of people in the train was 80 + 96 = 176.
After 8 males got off, the new number of people in the train is 176 - 8 = 168.
Hence, the number of people in the train now is 168.
To solve this problem, let's first assume the original number of males and females on the train as 5x and 6x, respectively, where x is a common factor.
After 8 males got off the train, the updated number of males becomes 5x - 8 and the number of females remains the same, 6x.
Now, the ratio of males to females is given as 3:4, which means the updated number of males divided by the number of females is equal to 3/4. We can write this as:
(5x - 8) / 6x = 3/4
Now, let's solve this equation to find the value of x.
Cross-multiplying, we get:
4 * (5x - 8) = 3 * (6x)
20x - 32 = 18x
Moving the variables to one side and the constants to the other side, we have:
20x - 18x = 32
2x = 32
Dividing both sides by 2, we get:
x = 16
Now, we can substitute the value of x back into one of the original equations to find the number of people in the train.
Number of males = 5x = 5 * 16 = 80
Number of females = 6x = 6 * 16 = 96
Therefore, the total number of people in the train now is 80 males + 96 females = 176 people.