If 0 ≤ x ≤ 5 and 5 ≤ y ≤ 10, then maximum value of (x / y) will be

When a fraction's numerator and denominator each vary independently within their own allowed ranges, the fraction reaches its largest value when the numerator takes its own maximum and the denominator takes its own minimum (for positive values, a bigger numerator or a smaller denominator each make the ratio bigger).

1. x lies in the range 0 ≤ x ≤ 5, so the largest value x can take is 5.

2. y lies in the range 5 ≤ y ≤ 10, so the smallest value y can take is 5.

3. Substituting these extreme values gives x / y = 5 / 5 = 1.

Checking other combinations confirms this is the largest attainable value: x = 5, y = 10 gives 1/2, and x = 0, y = 5 gives 0 — both smaller than 1, so 1 is indeed the maximum value of x / y over the given ranges.