What is the fourth proportional to the numbers 72, 168 and 150?

Introduction / Context:
This question uses the definition of fourth proportional, another classical term from ratio and proportion. It is a direct skill check: given three numbers, we are asked to find the fourth proportional. Such questions are straightforward once the definition and formula are remembered, and they form a base for more complicated proportional reasoning in aptitude exams.

Given Data / Assumptions:

• First three numbers are 72, 168 and 150.
• We need to find the fourth proportional.
• We use the standard proportional definition.

Concept / Approach:
If a, b, c and d are four numbers such that a : b = c : d, then d is called the fourth proportional to a, b and c. The proportion a : b = c : d leads to the equation a * d = b * c, hence d = (b * c) / a. In this problem, a = 72, b = 168 and c = 150, so d = (168 * 150) / 72. Once we compute d, we select the matching option.

Step-by-Step Solution:
Let the fourth proportional to 72, 168 and 150 be d.By definition, 72 : 168 = 150 : d.So 72 * d = 168 * 150.Compute 168 * 150 = 168 * (100 + 50) = 16800 + 8400 = 25200.Thus 72 * d = 25200.So d = 25200 / 72.Simplify: divide numerator and denominator by 8 to get 3150 / 9 = 350.Therefore, d = 350.

Verification / Alternative check:
Check the proportion 72 : 168 = 150 : 350.Simplify 72 : 168 by dividing by 24 to get 3 : 7.Simplify 150 : 350 by dividing by 50 to get 3 : 7.Since both ratios are equal, 350 is the correct fourth proportional.

Why Other Options Are Wrong:
Values such as 450, 300, 400 or 250 do not maintain the equality 72 : 168 = 150 : d. For example, if d = 300, then 150 : 300 = 1 : 2 which is not equal to 3 : 7. Only 350 gives the same simplified ratio as 72 : 168, so the other options are incorrect.

Common Pitfalls:
Students often confuse fourth proportional with third proportional or use the wrong formula. Some may attempt to average numbers or simply guess close values. The proper approach is to write a : b = c : d, cross multiply, and solve for d. Keeping this template in mind ensures reliable solutions to all similar problems.

Final Answer:
The fourth proportional to 72, 168 and 150 is 350.