A distance X km is covered by two different trains with velocity y (in km/hr) and ky (in km/hr) in y and y + 3 hours respectively.
If y < 13 then k is less than : [amp_mcq option1="5/8" option2="11/16" option3="3/4" option4="13/16" correct="option4"]
For the second train: Distance X = velocity * time = (ky) * (y + 3).
Since the distance X is the same:
y² = ky(y + 3)
Given y is a velocity and time, y > 0. We can divide both sides by y:
y = k(y + 3)
y = ky + 3k
y – ky = 3k
y(1 – k) = 3k
y = 3k / (1 – k)
We are given that y < 13. So, 3k / (1 - k) < 13 For the velocity ky and time (y+3) to be positive, k must be positive (since y>0 and y+3>0). Also, for the denominator (1-k) to result in a positive value for y (which must be positive as it’s velocity/time), (1-k) must be positive, meaning k < 1. So, 0 < k < 1. Since 0 < k < 1, (1 - k) is positive. We can multiply the inequality by (1 - k) without changing the direction: 3k < 13(1 - k) 3k < 13 - 13k 3k + 13k < 13 16k < 13 k < 13/16. Thus, if y < 13, then k is less than 13/16.