In a group of 120 people, one-fifth are men, one-fourth are women and the rest are children The average age of women is five-sixth of the average age of men. If average age of men is 60 years, what is the average age of the group? (Work & Time)

প্রশ্নে বলা হচ্ছে যে, 120 জন লোকের একটি দলে $\frac{1}{5}$ অংশ পুরুষ $\frac{1}{4}$ অংশ নারী এবং বাকি অংশ শিশু। পুরুষদের গড়  বয়সের $\frac{5}{6}$ অংশ হলো নারীদের গড় বয়স। পুরুষদের গড় বয়স 60 হলে ঐ দলের লোকদের গড় বয়স কত?

$$\begin{gathered} Number of men = \left(120 \times \frac{1}{5}\right) = 24 \& women = \left(120 \times \frac{1}{4}\right) =30 \\ \therefore The total number of children = 120 (24+30) = 120-54 = 66 \\ As the average age of men = 60 years \\ \therefore So, the average age of women = \left(60 \times \frac{5}{6}\right) = 50 years \\ Now, let x be the average age of children. \\ \therefore Total age of the group will be = (24 \times 60) + (30 \times 50) + (66 \times x) = 1,440 + 1,500 + 66x \\ \therefore Average of the group \frac{1440 + 1500 + 66x}{120} = \frac{2940 + 66x}{120} = \frac{6 \left(490 + 11\right)}{120} = \frac{490 + 11x}{20} years. \end{gathered}$$