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07 Apr 2022, 04:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
90% (01:32) correct
10%
(01:51)
wrong
based on 40
sessions
History
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Time
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Not Attempted Yet
The sum of the ages of a mother and a daughter is 40 years. Also, 5 years ago, the mother’s age was 9 times the age of the daughter. The present age of mother and daughter respectively are :
(A) 42 yrs, 8 yrs.
(B) 40 yrs, 10 yrs
(C) 38 yrs, 12 yrs.
(D) 35 yrs, 15 yrs
(E) 32 yrs, 8 yrs
(A) 42 yrs, 8 yrs.
(B) 40 yrs, 10 yrs
(C) 38 yrs, 12 yrs.
(D) 35 yrs, 15 yrs
(E) 32 yrs, 8 yrs
08 Apr 2022, 22:01
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In any question on ages, start by assuming variables for the present ages of the people mentioned. Having variables makes it easy to create equations.
Let us make a table of the ages of the mother and the daughter:
9th Apr 2022 - Post 2.png [ 7.05 KiB | Viewed 2487 times ]
From the first statement, we have M + D = 40.
From the second statement, we have (M-5) = 9 (D-5). Simplifying this equation, we have,
M = 9 D – 40. Substituting this in the first equation, we have,
9D – 40 + D = 40
Simplifying and solving for D, we have D = 8 and hence, M = 32.
The correct answer option is E.
While the above represents a very traditional approach of solving this question, a more logical approach would be to understand the situation in terms of the numbers given in the options.
As per the question, 5 years ago, (M-5) = 9 (D-5). Therefore, 5 years ago, the mother’s age should be a multiple of 9.
Remember that all the answer options represent the present ages of the mother and the daughter, in that order.
Therefore, in every option, we subtract 5 from the first number and check which one gives us a multiple of 9. Clearly, that happens only in E.
Let us make a table of the ages of the mother and the daughter:
Attachment:
9th Apr 2022 - Post 2.png [ 7.05 KiB | Viewed 2487 times ]
From the first statement, we have M + D = 40.
From the second statement, we have (M-5) = 9 (D-5). Simplifying this equation, we have,
M = 9 D – 40. Substituting this in the first equation, we have,
9D – 40 + D = 40
Simplifying and solving for D, we have D = 8 and hence, M = 32.
The correct answer option is E.
While the above represents a very traditional approach of solving this question, a more logical approach would be to understand the situation in terms of the numbers given in the options.
As per the question, 5 years ago, (M-5) = 9 (D-5). Therefore, 5 years ago, the mother’s age should be a multiple of 9.
Remember that all the answer options represent the present ages of the mother and the daughter, in that order.
Therefore, in every option, we subtract 5 from the first number and check which one gives us a multiple of 9. Clearly, that happens only in E.
19 Feb 2024, 03:45
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In this exercise, I got confused because the text did not directly specify that the daughter's age was decreased by 5 years in the second part of the question.
Once I used the decreased age, everything went fine.
Quote:
Once I used the decreased age, everything went fine.
