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1. Two numbers are in the ratio 17 : 45, One - third of the smaller is less than $\frac{1}{5}$ of the bigger by 15. The smaller number is = ?

A. $25 \frac{1}{2}$

B. $67 \frac{1}{2}$

C. $76 \frac{1}{2}$

D. $86 \frac{1}{2}$

Solution:

\begin{aligned} A : B \\ 17 : 45 \\ 17 x : 45 x \\ Given \\ \Rightarrow 17 x \times \frac{1}{3} + 15 = 45 x \times \frac{1}{5} \\ \Rightarrow \frac{17 x + 45}{3} = 9 x \\ \Rightarrow 17 x + 45 = 27 x \\ \Rightarrow 10 x = 45 \\ \Rightarrow x = \frac{45}{10} \\ ∴ Smaller number is \\ = \frac{45}{10} \times 17 \\ = \frac{765}{10} \\ = 76 \frac{1}{2} \end{aligned}

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