If the difference between the reciprocal of a positive proper fraction and the fraction itself be $$\frac{9}{20}$$, then the fraction is :
A. $$\frac{3}{5}$$
B. $$\frac{4}{5}$$
C. $$\frac{5}{4}$$
D. $$\frac{3}{10}$$
Answer: Option B
Solution(By Examveda Team)
Let the fraction be $$\frac{a}{1}$$Then,
$$\eqalign{ & \Leftrightarrow \frac{1}{a} - a = \frac{9}{{20}} \cr & \Leftrightarrow \frac{{1 - {a^2}}}{a} = \frac{9}{{20}} \cr & \Leftrightarrow 20 - 20{a^2} = 9a \cr & \Leftrightarrow 20{a^2} + 9a - 20 = 0 \cr & \Leftrightarrow 20{a^2} + 25a - 16a - 20 = 0 \cr & \Leftrightarrow 5a\left( {4a + 5} \right) - 4\left( {4a + 5} \right) = 0 \cr & \Leftrightarrow \left( {4a + 5} \right)\left( {5a - 4} \right) = 0 \cr & \Leftrightarrow a = \frac{4}{5}\,\,\,\,\,\,\,\,\left[ {\because a \ne - \frac{5}{4}} \right] \cr} $$
Related Questions on Problems on Numbers
If one-third of one-fourth of a number is 15, then three-tenth of that number is:
A. 35
B. 36
C. 45
D. 54
E. None of these
A. 9
B. 11
C. 13
D. 15
E. None of these
A. 3
B. 4
C. 9
D. Cannot be determined
E. None of these
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