10 women can do a piece of work in 6 days, 6 men can do same work in 5 days and 8 children can do it in 10 days. What is the ratio of the efficiency of a woman, a man and a child respectively?

Let the efficiency of a woman, a man and a child respectively be $$w,m,c$$

10 women can do the work in 6 days

=> 1 woman's 1 day's work = $$w=\frac{1}{10\times6}=\frac{1}{60}$$

Similarly, $$m=\frac{1}{30}$$ and $$c=\frac{1}{80}$$

$$\therefore$$ $$w:m:c=\frac{1}{60}:\frac{1}{30}:\frac{1}{80}$$

= $$\frac{1}{6}:\frac{1}{3}:\frac{1}{8}$$

Now, multiplying by L.C.M.(6,3,8) = 24

= $$24\times(\frac{1}{6}:\frac{1}{3}:\frac{1}{8})$$

= $$4:8:3$$

=> Ans - (D)