16 men can finish a piece of work in 49 days. 14 men started working and 8 days they could finish certain amount of work. If it is required to finish the remaining work in 24 days. How many more men should be added to the existing workforce ?
Correct Answer: 14
$$\eqalign{ & {\text{Given,}} \cr & {{\text{M}}_1} = 16{\text{ , }}{{\text{M}}_2} = ? \cr & {{\text{D}}_1} = 49{\text{ , }}{{\text{D}}_2} = 24 \cr & {{\text{W}}_1} = 1{\text{ ,}}{{\text{W}}_2} = ? \cr & {\text{According to the question,}} \cr & \frac{{{{\text{M}}_1}{{\text{D}}_1}}}{{{{\text{W}}_1}}}{\text{ = }}\frac{{{{\text{M}}_2}{{\text{D}}_2}}}{{{{\text{W}}_2}}} \cr & \Rightarrow \frac{{16 \times 49}}{1} = \frac{{14 \times 8}}{{{{\text{W}}_2}}} \cr & \Rightarrow {{\text{W}}_2} = \frac{{14 \times 8}}{{16 \times 49}} \cr & \Rightarrow {{\text{W}}_2} = \frac{1}{7} \cr & {\text{Remaining work}} \cr & = \left( {1 - \frac{1}{7}} \right) \cr & = \frac{6}{7} \cr & {\text{Again,}}\frac{{{{\text{M}}_1}{{\text{D}}_1}}}{{{{\text{W}}_1}}}{\text{ = }}\frac{{{{\text{M}}_2}{{\text{D}}_2}}}{{{{\text{W}}_2}}} \cr & \Rightarrow \frac{{16 \times 49}}{1} = \frac{{{{\text{M}}_2} \times 24}}{{\frac{6}{7}}} \cr & \Rightarrow 16 \times 49 = \frac{{{{\text{M}}_2} \times 24 \times 7}}{6} \cr & \Rightarrow 16 \times 49 = {{\text{M}}_2} \times 4 \times 7 \cr & \Rightarrow {{\text{M}}_2} = \frac{{16 \times 49}}{{4 \times 7}} \cr & \Rightarrow {{\text{M}}_2} = 28 \cr & \therefore {\text{Number of additional men}} \cr & = \left( {28 - 14} \right) \cr & = 14 \cr} $$