In a pharmaceutical company, a medicine is prepared by mixing two different solutions of medicines. Four varieties of medicines are available viz A, B, C and D having concentration of the chemical as 20%, 30%, 40% and 60%. A new medicine, 50% of the chemical, is to be made. If medicines A, B, C and D cost Rs. 400, Rs. 600, Rs. 800 and Rs. 1000 per litre respectively. What is the minimum cost of making 1 litre of required medicine?a)R s . 825b)R s. 870c)R s. 867d)R s. 900e)None of theseCorrect answer is option 'E'. Can you explain this answer?

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In a pharmaceutical company, a medicine is prepared by mixing two different solutions of medicines. Four varieties of medicines are available viz A, B, C and D having concentration of the chemical as 20%, 30%, 40% and 60%. A new medicine, 50% of the chemical, is to be made. If medicines A, B, C and D cost Rs. 400, Rs. 600, Rs. 800 and Rs. 1000 per litre respectively. What is the minimum cost of making 1 litre of required medicine?

a)
R s . 825
b)
R s. 870
c)
R s. 867
d)
R s. 900
e)
None of these

Correct answer is option 'E'. Can you explain this answer?

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In a pharmaceutical company, a medicine is prepared by mixing two diff...

Only in medicine D, concentration of the chemical is more than 50%. Hence, medicine D must be used.
Assume that another medicine of concentration x% and cost y is used.
If we look at medicines A, B and C, if x% is the concentration, y = 20x

Whatever medicine is used with D, y = 20x

The ratio of another medicine to medicine D

It is clear that 20 < x < 40

i.e.,x = 20

Hence, option 5.
Alternatively;

Case I:

Only in medicine D, concentration of the chemical is more than 50%. Hence, medicine D must be used. If medicine A is used with medicine D; The ratio of medicine A to medicine D

Case II:

If medicine B is used with medicine D; The ratio of medicine B to medicine D

Case III:

If medicine C is used with medicine D; The ratio of medicine C to medicine D

The minimum cost of making 1 litre of the required medicine is Rs. 850.
Hence, option 5.

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