Multiple choice

A jar contain a mixture of milk and water in the ratio 3 : 2. The volume of the contents is increased by 50% by adding water to it. From the resultant solution 30 L is withdrawn and then replaced with water. The resultant ratio of milk and water in the final solution is 3 : 7. Find the original volume of milk in the solution? एक जार में दूध और पानी का अनुपात 3: 2 हैं। पानी की कुछ मात्रा मिलाने पर इस मिश्रण के आयतन में 50 प्रतिशत की वृद्धि होती हैं। प्राप्त मिश्रण से यदि 30 लीटर मिश्रण निकालकर पानी से बदल दिया जाये तब नए मिश्रण में दूध और पानी के बीच अनुपात 3: 7 होगा। वास्तविक मिश्रण में दूध का आयतन ज्ञात कीजिये ?

  1. 120

  2. 80

  3. 48

  4. 90

  5. 180

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

Let initial volumes be 3x milk and 2x water (total 5x). After adding 50% water (2.5x), new ratio is 3x:4.5x, total = 7.5x. After removing 30L and replacing with water: milk removed = 30 × 3/7.5 = 12L, water removed = 30 × 4.5/7.5 = 18L. Remaining: milk = 3x-12, water = 4.5x-18. After adding 30L water: milk = 3x-12, water = 4.5x+12. New ratio (3x-12)/(4.5x+12) = 3/7. Solving: 21x-84 = 13.5x+36, so 7.5x = 120, x = 16. Initial milk = 3×16 = 48L (option C).