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Select the correct answerThe ratio of ages of two persons is 5 : 9 and the age of one of them is greater than the other by 40 years. The sum of their ages in year is?Options150180140160

Question

Select the correct answerThe ratio of ages of two persons is 5 : 9 and the age of one of them is greater than the other by 40 years. The sum of their ages in year is?Options150180140160

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Solution 1

Let's solve this step by step:

  1. The ratio of the ages of two persons is 5:9. This means that if the age of the younger person is 5x, the age of the older person is 9x.

  2. The problem also states that the age of one of them is greater than the other by 40 years. So, 9x - 5x = 40.

  3. Solving this equation gives x = 20.

  4. The sum of their ages is 5x + 9x = 14x.

  5. Substituting x = 20 into this equation gives 14*20 = 280.

So, the sum of their ages is 280 years. However, this option is not available in the given options. There might be a mistake in the problem or the options.

This problem has been solved

Solution 2

Let's solve this step by step:

  1. The ratio of the ages of two persons is 5:9. This means that for every 5 years of age the younger person has, the older person has 9 years.

  2. The problem also states that the age of one of them is greater than the other by 40 years. This difference corresponds to the difference in the ratio, which is 9 - 5 = 4.

  3. Therefore, 4 units in the ratio correspond to a 40-year difference in their ages. This means that 1 unit in the ratio corresponds to 40/4 = 10 years.

  4. To find the sum of their ages, we need to add up all the units in the ratio, which is 5 + 9 = 14 units.

  5. Since 1 unit corresponds to 10 years, 14 units correspond to 14 * 10 = 140 years.

So, the sum of their ages is 140 years.

This problem has been solved

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