Question
10 less than a given number K, 10 more than the given
number K, and 38 more than the given number K are in continued proportion. Find the given number K. where K > 0.Solution
Let the number be =k - 10, k + 10 and k + 38 According to the question- (k-10)/ (k + 10) = (k + 10)/ (k + 38) Ā (k + 10)2 = (k - 10) (k + 38) Ā (kĀ² + 2 x k x 10 + 100) = (kĀ² + 38k - 10k - 380) (kĀ² + 20k + 100) = (kĀ² + 28k-380) (28k-20k) = (380 + 100) Ā 8k = 480 Ā k = 480/8 Ā k = 60 Ā The value of k is 60.
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