Question
Download Solution PDFThe ratio between the present ages of Amit and Amita is 7 : 5, respectively. The ratio between Amit’s age 5 years ago and Amita’s age 5 years hence is 1 : 1. After how many years from now will the age of Amit and Amita together be 72 years?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The ratio between the present ages of Amit and Amita = 7:5
The ratio between Amit's age 5 years ago and Amita's age 5 years hence = 1:1
Calculation:
Let the present ages of Amit and Amita be 7x and 5x, respectively.
Amit's age 5 years ago = 7x - 5
Amita's age 5 years hence = 5x + 5
Given, (7x - 5) / (5x + 5) = 1 / 1
7x - 5 = 5x + 5
After how many years from now will the age of Amit and Amita together be 72 years?
(7x + n) + (5x + n) = 72
⇒ 7x - 5 = 5x + 5
⇒ 7x - 5x = 5 + 5
⇒ 2x = 10
⇒ x = 5
Present age of Amit = 7x = 7(5) = 35 years
Present age of Amita = 5x = 5(5) = 25 years
After n years, (35 + n) + (25 + n) = 72
⇒ 60 + 2n = 72
⇒ 2n = 12
⇒ n = 6
The correct answer is option 2: 6 years
Last updated on Jul 16, 2025
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