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If 9:12::12:k, then find the value of k+1.
18
17
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16
17
In a continuous proportion a:b::b:k, the mean proportional b satisfies b2=a├Чk. Thus, k=ab2тАЛ=9122тАЛ.
A proportion 9 : 12 :: 12 : k is given.
a:b::c:dтЯ╣a├Чd=b├Чc
In a continuous proportion a:b::b:k, the mean proportional b satisfies b2=a├Чk. Thus, k=ab2тАЛ=9122тАЛ.
Many students mistake the proportion rule and solve as 129тАЛ=12kтАЛ, failing to treat k as the fourth proportional.
Set up the proportion equation
Given the ratio 9:12::12:k, we can write this as a fractional equivalence: 129тАЛ=k12тАЛ
129тАЛ=k12тАЛ
Solve for k
By cross-multiplying, we get 9k=12├Ч12. Simplifying, 9k=144, so k=9144тАЛ=16.
k=16
Calculate the final value
The question asks for the value of k+1. Substituting k=16, we get 16+1=17.
k+1=17
B is correct because the calculated value of k is 16, and k+1 is 17.
This is a fundamental concept in Ratio and Proportion which frequently appears in DI (Data Interpretation) and simplification questions.
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