₹2100 is divided among P, Q and R in such a way that P's share is half of the combined share of Q and R, and Q's share is one-fourth of the combined share of P and R. By what amount is R's share more than that of P?

According to the question,

$$P+Q+R=2100$$......................(1)

P's share is half of the combined share of Q and R

$$=$$>  $$P=\frac{\ Q+R}{2}$$

$$=$$>  $$2P=\ Q+R$$..........................(2)

From (1) and (2),  $$P+2P=2100$$

$$=$$>  $$P=700$$

Q's share is one-fourth of the combined share of P and R

$$=$$>  $$Q=\frac{\ P+R}{4}$$

$$=$$>  $$4Q=\ P+R$$..........................(3)

From (1) and (3),  $$Q+4Q=2100$$

$$=$$>  $$Q=420$$

Substituting $$P=700$$ and $$Q=420$$ in equation(1)

  $$700+420+R=2100$$

$$=$$>  $$R=980$$

Now,  $$R-P=980-700=280$$

So, R's share is 280 more than P's share

Hence, the correct answer is Option D