A certain sum is divided among p, q and r in a manner that for every rupee that p gets, q gets 75 paise and for every rupee that q gets, r gets 50 paise. If r’s share in the total sum is ₹ 36, then find the share of p.

A certain sum is divided among p, q and r in a manner that for every rupee that p gets, q gets 75 paise, 

$$\frac{p}{q}=\frac{100}{75}=\frac{4}{3}$$

and for every rupee that q gets, r gets 50 paise.

$$\frac{q}{r}=\frac{100}{50}=\frac{2}{1}$$

To compare the ratio we need to equate both the ratios and make the value of q equal in both.

So multiplying both denominator and numerator we get,

$$\frac{q}{r}=\frac{6}{3}$$
$$\frac{p}{q}=\frac{8}{6}$$

Therefore, p : q : r :: 8 : 6 : 3

According to question,

If r’s share in the total sum is ₹ 36, 

$$3 units = 36$$

$$1 unit = 12$$

Therefore, p's share = $$8\times12 = 96$$

Option A is correct.