Which of the following numbers does not lie between $$\frac{4}{5}$$ and $$\frac{7}{13}$$ = ?
(A) $$\frac{1}{2}$$
(B) $$\frac{2}{3}$$
(C) $$\frac{3}{4}$$
(D) $$\frac{5}{7}$$
Solution:
$$\frac{4}{5}$$ = 0.8 $$\frac{7}{13}$$ = 0.53 $$\frac{1}{2}$$ = 0.5 $$\frac{2}{3}$$ = 0.66 $$\frac{3}{4}$$ = 0.75 $$\frac{5}{7}$$ = 0.714 Clearly, 0.5 does not lie between 0.53 and 0.8 ∴ $$\frac{1}{2}$$ does not lie between $$\frac{4}{5}$$ and $$\frac{7}{13}$$
The numerator of a fraction is decreased by 25% and the denominator is increased by 250%. If the resultant fraction is $$\frac{6}{5}$$, what is the original fraction ?
(A) $$\frac{22}{5}$$
(B) $$\frac{24}{5}$$
(C) $$\frac{27}{6}$$
(D) $$\frac{28}{5}$$
Solution:
Let original fraction be $$\frac{a}{b}$$ Now, according to the question, $$\eqalign{ & \Leftrightarrow \frac{{a - a \times \frac{{25}}{{100}}}}{{b + b \times \frac{{250}}{{100}}}} = \frac{6}{5} \cr & \Rightarrow \frac{{0.75a}}{{3.50b}} = \frac{6}{5} \cr & \Rightarrow \frac{a}{b} = \frac{6}{5} \times \frac{{3.50}}{{0.75}} \cr & \Rightarrow \frac{a}{b} = \frac{{6 \times 350 \times 100}}{{5 \times 75 \times 100}} \cr & \Rightarrow \frac{a}{b} = \frac{{28}}{5} \cr} $$
88.
$$\frac{{4.2 \times 4.2 - 1.9 \times 1.9}}{{2.3 \times 6.1}}$$ ÃÂÃÂ ÃÂÃÂ is equal to: