Question:
The sum of the ages of a mother and her daughter is 50 years. Also, 5 years
ago, the mother’s age was 7 times the age of the daughter. What are the present
ages of the mother and the daughter? [एक माता और उसकी पुत्री की उम्रों का योगफल 50
वर्ष है. 5 वर्ष पहले माता की आयु पुत्री की आयु की 7 गुणी थी. बताएं कि आज माता
और पुत्री की आयु क्या है?] [Ans. (c) 40 yrs, 10 yrs]
(a) 45 yrs, 5 yrs (b) 42 yrs, 8 yrs (c) 40 yrs, 10 yrs (d) 41 yrs, 9 yrs (e) none of these
Solution:
Detailed
Explanation:
Concept: When the
sum of the ages of two persons goes to 5 years ago, it is reduced by 10 years
(as the age of each of the persons is reduced by 5 years)
First Method:
Given that the sum of the ages of a mother and her daughter is 50 years (at
present), so the sum of their ages 5 years ago was 50-10 = 40 years.
Also given that
the ratio of the ages of the mother and her daughter 5 years ago was 7:1, so
that the sum is 8 (in terms of ratio).
8 ≡ 40 years
1 ≡? = 5 years (the
age of daughter 5 years ago)
7 ≡? = 35 years (the
age of mother 5 years ago)
Therefore, the
present age of mother is 35+5 = 40 years and the present age of daughter is 5+5
= 10 years. Ans.
Second Method: Let
the ages of daughter and mother 5 years ago were “x” years and “7x” years. So, their present ages are respectively (x+5)
years and (7x+5) years.
Given that the sum
of the present ages of mother and her daughter is 50 years, so
(7x+5) + (x + 5) =
50 or, 8x = 40 or, x = 5
Therefore, the
present age of mother = 7×5+5 = 40 yrs and the present age of daughter = 5+5 =
10 yrs Ans.
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