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When 'p' is subtracted from each of 18, 15, 23 and 16, then the numbers so obtained in this order are in proportion. What is the value of \(\left( {p - \frac{1}{4}} \right)\)?1. 142. \(\frac{{51}}{4}\)3. 114. \(\frac{{57}}{4}\) |
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Answer» Correct Answer - Option 1 : 14 Given: When 'p' is subtracted from each of 18, 15, 23 and 16, then the numbers so obtained in this order are in proportion. Concept used: Ratio and proportion Calculation: As per the question, ⇒ \(\frac{{18 - p}}{{15 - p}} = \frac{{23 - p}}{{16 - p}}\) ⇒ (18 - p) (16 - p) = (15 - p) ( 23 - p) ⇒ 288 - 34p + p2 = 345 - 38p + p2 ⇒ 4p = 57 ⇒ p = 57/4 We need to find \(\left( {p - \frac{1}{4}} \right)\) ⇒ 57/4 - 1/4 ⇒ 56/4 = 14
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