Question 88

If $$a_1, a_2, a_3$$ and $$a_4$$ is the decreasing order of the elements in $$\left\{\frac{2}{7}, \frac{7}{15}, \frac{5}{8}, \frac{9}{23}\right\}$$ then $$a_1 - a_4 =$$

Solution

$$\frac{2}{7}=0.285$$

$$\frac{7}{15}=0.47$$

$$\frac{5}{8}=0.625$$

$$\frac{9}{23}=0.391$$

Decreasing order of the fractions is $$\frac{5}{8}$$, $$\frac{7}{15}$$, $$\frac{9}{23}$$, $$\frac{2}{7}$$

$$\Rightarrow$$ $$a_1=\frac{5}{8}$$ and $$a_4=\frac{2}{7}$$

$$\therefore\ $$ $$a_1-a_4=\frac{5}{8}-\frac{2}{7}=\frac{35-16}{56}=\frac{19}{56}$$

Hence, the correct answer is Option D

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