Question

In what ratio must water be mixed with milk costing Rs. 32 per litre to obtain a mixture worth Rs. 28 per litre? (Water is free.)

• A. 1 : 8
• B. 1 : 7
• C. 2 : 7
• D. 1 : 6

Hint:

Assume the final mixture is exactly one litre and write a direct cost-balance equation between water and milk instead of using the alligation cross method.

Answer 1

The Correct Option is B

Step 1: Consider exactly 1 litre of the final mixture, containing $w$ litres of water (cost 0) and $m$ litres of milk (cost Rs. 32/litre), with $w+m=1$.
Step 2: The total cost of this 1 litre of mixture must equal $28\times(w+m)=28\times1=28$. Also, total cost $=0\times w+32\times m=32m$.
Step 3: $32m=28\Rightarrow m=\dfrac{28}{32}=\dfrac{7}{8}$ litres, so $w=1-\dfrac{7}{8}=\dfrac{1}{8}$ litres.
Step 4: Ratio of water to milk $=w:m=\dfrac{1}{8}:\dfrac{7}{8}=1:7$.
\[\boxed{1:7}\]