A chemist prepared 50 grams of a medicine by mixing two ingredients 'P' and 'Q'. Rate of 'P' is ₹ 150 per 10 gm and that of 'Q' is ₹ 500 per 100 gm. 'P' and 'Q' are mixed in such a way that the cost of the resulting medicine is ₹ 12 per gm. What is the quantity of 'P' (in grams) in the medicine ?

Correct option is D

Given:

Total mass of the medicine = 50 grams

Rate of 'P' = ₹ 150 per 10 gm (i.e., ₹ 15 per gm)

Rate of 'Q' = ₹ 500 per 100 gm (i.e., ₹ 5 per gm)

Cost of the resulting medicine = ₹ 12 per gm

Solution:
Let the quantity of 'P' be x grams and the quantity of 'Q' be (50 - x) grams.

The total cost of the medicine can be written as:
Cost of medicine = Cost of P + Cost of Q

Cost of P = 1$$5x \quad (\text{since 'P' costs ₹ 15 per gram})$$​​
​$$\text{Cost of Q} = 5(50 - x) \quad (\text{since 'Q' costs ₹ 5 per gram})$$​​

The total cost of the 50 grams of the medicine is:
Total cost = 12 $$\times 5$$​0 = ₹ 600

Thus, the equation becomes:
15x + 5(50 - x) = 600

15x + 250 - 5x = 600
10x + 250 = 600
10x = 600 - 250
10x = 350
x  = 35

The quantity of 'P' in the medicine is 35 grams.