A 90-litre mixture contains milk and water in the ratio 7 : 2. If 'x' litres of milk and 'x' litres of water are added to the mixture, the new ratio of milk to water becomes 5 : 2. What is the value of 'x'?
13.33 litres
Step 1 — Initial quantities (total 90 L, ratio 7 : 2 → 9 parts):
\(\text{Milk} = \dfrac{7}{9} \times 90 = 70 \text{ L}, \quad \text{Water} = \dfrac{2}{9} \times 90 = 20 \text{ L}\)
Step 2 — After adding x L of each:
\(\text{New milk} = 70 + x, \quad \text{New water} = 20 + x\)
Step 3 — Apply the new ratio condition:
\(\dfrac{70 + x}{20 + x} = \dfrac{5}{2}\)
Step 4 — Cross-multiply and solve:
\(2(70 + x) = 5(20 + x)\)
\(140 + 2x = 100 + 5x \quad \Rightarrow \quad 40 = 3x \quad \Rightarrow \quad x = \dfrac{40}{3} \approx 13.33 \text{ L}\)
Hence, the answer is option A.
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