Multiple choice

A jar contained a mixture of two liquids P and Q in the ratio 5:2. When 14 litres of the mixture was taken out and 14 litres of liquid Q was poured in to the jar, this ratio becomes 7:9 .The quantity of liquid P contained in the Jar was - एक जार मिश्रण से भरा हुआ है, जिसमें दो द्रव P और Q का अनुपात 5:2 है । जब 14 लीटर मिश्रण इससे निकालकर और 14 लीटर द्रव Q इसमें डाला जाता है तो अनुपात 7:9 होंजाता है। जार में द्रव P की मात्रा थी-

  1. 10 litre /लीटर

  2. 15 litre /लीटर

  3. 20 litre /लीटर

  4. 25 litre /लीटर

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P = 5x, Q = 2x. After removing 14 litres: remaining P = 5x - (14 × 5/7) = 5x - 10, remaining Q = 2x - (14 × 2/7) = 2x - 4. After adding 14 litres Q: new Q = 2x - 4 + 14 = 2x + 10. New ratio P:Q = 7:9, so (5x - 10)/(2x + 10) = 7/9. Cross-multiply: 9(5x - 10) = 7(2x + 10), giving 45x - 90 = 14x + 70, so 31x = 160, x = 160/31. P = 5x = 800/31 ≈ 25.8 litres, approximately 25 litres. Option D is correct.