If $$M = \frac{3}{7} \div \frac{6}{5} \times \frac{2}{3} + \frac{1}{5} \times \frac{3}{2}$$ and $$N = \frac{2}{5} \times \frac{5}{6} \div \frac{1}{3} + \frac{3}{5} \times \frac{2}{3} \div \frac{3}{5},$$ then what is the value of $$\frac{M}{N}$$?
A. $$\frac{{207}}{{560}}$$
B. $$\frac{{339}}{{1120}}$$
C. $$\frac{{113}}{{350}}$$
D. $$\frac{{69}}{{175}}$$
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & M = \frac{3}{7} \div \frac{6}{5} \times \frac{2}{3} + \frac{1}{5} \times \frac{3}{2} \cr & = \frac{3}{7} \times \frac{5}{6} \times \frac{2}{3} + \frac{3}{{10}} \cr & = \frac{5}{{21}} + \frac{3}{{10}} \cr & = \frac{{50 + 63}}{{210}} \cr & = \frac{{113}}{{210}} \cr & N = \frac{2}{5} \times \frac{5}{6} \div \frac{1}{3} + \frac{3}{5} \times \frac{2}{3} \div \frac{3}{5} \cr & = \frac{2}{5} \times \frac{5}{6} \times \frac{3}{1} + \frac{3}{5} \times \frac{2}{3} \times \frac{5}{3} \cr & = 1 + \frac{2}{3} \cr & = \frac{5}{3} \cr & \frac{M}{N} = \frac{{113}}{{210}} \div \frac{5}{3} \cr & = \frac{{113}}{{210}} \times \frac{3}{5} \cr & = \frac{{113}}{{350}} \cr} $$Related Questions on Simplification
A. 20
B. 80
C. 100
D. 200
E. None of these
A. Rs. 3500
B. Rs. 3750
C. Rs. 3840
D. Rs. 3900
E. None of these
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