It was intended that ₹2,820 be divided among A, B and C in the ratio of 3 : 4 : 5, but by mistake the distribution was made in the proportion of \(\tfrac{1}{3} \: \tfrac{1}{4} \: \tfrac{1}{5}\). How much does A gain by the error?
A man can do a work in 6 days, whereas a woman can do the same work in 12 days. In how many days will a man and a woman working together be able to do the same work?
The simplified value of \(\frac{1 \div \tfrac{3}{7}\,\text{of}\,\left(6 + 8 \times \overline{3 - 2}\right) + \left[ \tfrac{1}{5} \div \tfrac{7}{25} - \left\{ \tfrac{3}{7} + \tfrac{8}{14} \right\} \right]}{18 \div 10 - 4 + 32 \div (4 + 10 \div 2 - 1)}\) is:
\(-\tfrac{5}{42}\)
\(\tfrac{5}{42}\)
\(-\tfrac{5}{294}\)
\(\tfrac{5}{294}\)