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1. Find the whole number which when increased by 20 is equal to 69 times the reciprocal of the number.

A. 2.5

B. 3

C. 5

D. 7

Solution:

Let the required number be x
Then,

\begin{aligned} \Leftrightarrow x + 20 = \frac{69}{x} \\ \Leftrightarrow x^{2} + 20 x - 69 = 0 \\ \Leftrightarrow x^{2} + 23 x - 3 x - 69 = 0 \\ \Leftrightarrow x (x + 23) - 3 (x + 23) = 0 \\ \Leftrightarrow (x + 23) (x - 3) = 0 \\ \Leftrightarrow x = 3 [∵ x \neq - 23] \end{aligned}

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