Multiple choice

Vidyut has two conical flasks of capacities 3 and 5 litres, which are filled with mixtures of acid and water. In the smaller flask, 35% of the mixture is acid; and in the larger flask, 37% of the mixture is water. These flasks are then emptied into an 8.4-litre mug and the remaining volume is filled up with water. Find the percentage of acid in the mug.

  1. 50%

  2. 45%

  3. 55%

  4. 60%

  5. 75%
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A Correct answer
Explanation

Flask 1 (3L): 35% acid = 1.05L acid. Flask 2 (5L): 37% water = 63% acid. 5L * 0.63 = 3.15L acid. Total acid = 1.05 + 3.15 = 4.2L. Total mixture = 3 + 5 = 8L. The mug holds 8.4L, and the remaining 0.4L is water. Total acid remains 4.2L. Percentage of acid = (4.2 / 8.4) * 100 = 50%.

AI explanation

The total initial volume of the flasks is 8 litres, but the mug capacity is 8.4 litres, meaning 0.4 litres of water is added. The amount of acid in the smaller flask is 0.35 times 3 litres, which is 1.05 litres. The larger flask is 63 percent acid (since 37 percent is water), so its acid amount is 0.63 times 5 litres, which is 3.15 litres. The total acid in the mug is 1.05 plus 3.15, totaling 4.2 litres, which yields a concentration of 50 percent of the 8.4-litre mug.

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