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The fourth proportional to 15, 10 and 12 is:
12
10
6
8
8
Use the ratio equality property: 15 : 10 :: 12 : x. Since 15 is 1.5 times 10, x must be 12 / 1.5 = 8.
Three proportional values: a = 15, b = 10, c = 12. Let the fourth proportional be x.
baтАЛ=xcтАЛтЯ╣x=ab├ЧcтАЛ
Use the ratio equality property: 15 : 10 :: 12 : x. Since 15 is 1.5 times 10, x must be 12 / 1.5 = 8.
Many students incorrectly order the variables, setting them as 15: 10: 12: x and attempting 10 * 12 / 15, or forgetting the order defined by the problem statement (a, b, c).
Define the Proportionality
Given the terms 15, 10, and 12, they form a proportion as 15 : 10 = 12 : x, where x is the unknown fourth proportional.
15:10::12:x
Set up the Equation
Express the relationship as a ratio of fractions and solve for the unknown x.
1015тАЛ=x12тАЛ
Calculate the Result
Cross-multiply to find x: 15 * x = 10 * 12, which simplifies to 15 * x = 120.
x=15120тАЛ=8
D is correct because the calculation 10 ├Ч 12 / 15 results in 8.
This concept is fundamental to 'Direct Variation' and 'Unitary Method' problems in competitive exams.
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