Multiple choice

Given below are two statements: Statement I: The ratio of the son's age to the father's age is 1 : 5. The product of their ages is 245. The ratio of the son's age to the father's age after 9 years will be 3 : 5. Statement II: A milkman adds 30 litres of water to 70 litres of milk. After selling 1/5th of the total quantity, he adds water equal to the quantity he sold. The proportion of water to milk he sells now would be 28 : 72. In the light of the above statements, choose the correct answer from the options given below.

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement I is true. but Statement II is false.

  4. Statement I is false. but Statement II is true.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I: Let ages be x and 5x. x * 5x = 245 => 5x^2 = 245 => x^2 = 49 => x = 7. Ages are 7 and 35. After 9 years, ages are 16 and 44. Ratio 16:44 = 4:11, not 3:5. Statement I is false. Statement II: 70 milk, 30 water. Sell 1/5 (20L total), remaining 80L (56 milk, 24 water). Add 20L water. New mix: 56 milk, 44 water. Ratio water:milk = 44:56 = 11:14, not 28:72. Both are false.

AI explanation

For Statement I, if the ratio is 1 to 5 and the product is 245, the ages are the square root of 245/5, which is 7, and 35. After 9 years, their ratio would be (7 + 9) to (35 + 9), which simplifies to 16 to 44 or 4 to 11, not 3 to 5, making the statement false. For Statement II, after adding 30 liters of water to 70 liters of milk, selling 1/5th removes 6 liters of water and 14 liters of milk, leaving 24 liters of water and 56 liters of milk. Adding 20 liters of water makes the final ratio 44 to 56, which simplifies to 11 to 14, not 28 to 72. Both statements are false.

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