Question
Download Solution PDFA jar contains a mixture of 2 liquids P and Q in the ratio 4:1. When 10 litres of the mixture is taken out and 10 litres of liquid Q is poured into the jar, the ratio becomes 2:3. How many litres of the liquid P was contained in the jar?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A jar contains a mixture of two liquids P and Q in the ratio 4:1.
10 litres of the mixture is taken out, and 10 litres of liquid Q is added to the jar.
The new ratio becomes 2:3.
Formula used:
Let the initial quantity of liquid P be 4x and liquid Q be x.
After removing 10 litres of the mixture:
Liquid P removed = \(\frac{4}{5} \times 10\) = 8 litres.
Liquid Q removed = \(\frac{1}{5} \times 10\) = 2 litres.
The remaining quantities after removal:
Liquid P = 4x - 8.
Liquid Q = x - 2.
Adding 10 litres of liquid Q:
New liquid Q = (x - 2) + 10.
New ratio of P:Q = 2:3.
Equation: \(\frac{\text{Liquid P}}{\text{Liquid Q}} = \frac{2}{3}\)
Calculation:
\(\frac{4x - 8}{x - 2 + 10} = \frac{2}{3}\)
⇒ \(\frac{4x - 8}{x + 8} = \frac{2}{3}\)
⇒ 3(4x - 8) = 2(x + 8)
⇒ 12x - 24 = 2x + 16
⇒ 12x - 2x = 16 + 24
⇒ 10x = 40
⇒ x = 4
Initial liquid P = 4x = 4 × 4 = 16 litres.
∴ The correct answer is option (2).
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