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26 Dec 2019, 02:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
78% (02:37) correct
22%
(02:36)
wrong
based on 114
sessions
History
Date
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Not Attempted Yet
Six years back, the ratio of the ages of a husband and his wife was 6 : 5. Six years hence, their ages will be in the ratio 10 : 9. What is the ratio of their present ages.
A. 7 : 6
B. 8 : 7
C. 9 : 10
D. 18 : 15
E. 5 : 4
A. 7 : 6
B. 8 : 7
C. 9 : 10
D. 18 : 15
E. 5 : 4
26 Dec 2019, 04:11
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In a word problem on ages, I always assume the current ages using variables, because it gives me a head start in terms of developing the equations. Remember, in word problems, the biggest challenge is to develop the right equations and for that, you need to develop the right variables.
However, in this question, assuming their ages six years ago would make more sense since we have their ratio.
Six years ago, let age of husband = 6x and age of wife = 5x.
Then, six years hence, age of husband = 6x + 12 and age of wife = 5x + 12 (remember the difference between six years ago and six years hence is a total of 12 years).
But, question says that the ratio of the ages of the husband and the wife, 6 years hence, will be 10:9. Therefore, \(\frac{6x + 12 }{ 5x + 12}\) = \(\frac{10 }{ 9}\).
Solving for x, we get x = 3. This means, six years ago, their ages were 18 and 15 respectively. At this stage, if you go for option D, you have fallen for the easiest trap that you could fall into.
We need to find their present ages, not their ages 6 years ago. Additionally, 18:15 is the same as 6:5. Clearly, I won’t give you the ratio 6:5 as data and expect you to find the same as answer.
Present age of husband = 18 + 6 = 24 and present age of wife = 15 + 6 = 21.
The ratio of their present ages = 8:7. The correct answer option is B.
In a question on ages, be very careful about the trap answer options. After you get an answer, cross verify if your answer is right by reading the question statement. This will give you a chance to change your answer if needed.
Hope that helps!
However, in this question, assuming their ages six years ago would make more sense since we have their ratio.
Six years ago, let age of husband = 6x and age of wife = 5x.
Then, six years hence, age of husband = 6x + 12 and age of wife = 5x + 12 (remember the difference between six years ago and six years hence is a total of 12 years).
But, question says that the ratio of the ages of the husband and the wife, 6 years hence, will be 10:9. Therefore, \(\frac{6x + 12 }{ 5x + 12}\) = \(\frac{10 }{ 9}\).
Solving for x, we get x = 3. This means, six years ago, their ages were 18 and 15 respectively. At this stage, if you go for option D, you have fallen for the easiest trap that you could fall into.
We need to find their present ages, not their ages 6 years ago. Additionally, 18:15 is the same as 6:5. Clearly, I won’t give you the ratio 6:5 as data and expect you to find the same as answer.
Present age of husband = 18 + 6 = 24 and present age of wife = 15 + 6 = 21.
The ratio of their present ages = 8:7. The correct answer option is B.
In a question on ages, be very careful about the trap answer options. After you get an answer, cross verify if your answer is right by reading the question statement. This will give you a chance to change your answer if needed.
Hope that helps!
26 Dec 2019, 10:49
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Approach
- Six years back, the ratio of the ages of a husband and his wife was 6 : 5 => Assume ages be 6x and 5x.
- Present Age = 6x+6 : 5x+6
- Six years hence, their ages will be 6x+6+6 : 5x+6+6 which is equal to ratio as 10:9
- Equate the values \( \frac{6x+12}{5x+12}\) = \(\frac{10}{9}\) => \(x = 3\)
- Ratio of their present ages =\( \frac{6(3)+6}{5(3)+6}\) = \(\frac{24}{21 }\)= \(\frac{8}{7}\)
IMO Option B!
- Six years back, the ratio of the ages of a husband and his wife was 6 : 5 => Assume ages be 6x and 5x.
- Present Age = 6x+6 : 5x+6
- Six years hence, their ages will be 6x+6+6 : 5x+6+6 which is equal to ratio as 10:9
- Equate the values \( \frac{6x+12}{5x+12}\) = \(\frac{10}{9}\) => \(x = 3\)
- Ratio of their present ages =\( \frac{6(3)+6}{5(3)+6}\) = \(\frac{24}{21 }\)= \(\frac{8}{7}\)
IMO Option B!
