Question
Download Solution PDF5 years ago, the sum of my mother's and my ages was 40 years. Now the ratio of our ages is 4 : 1. What is my mother's age?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
5 years ago, the sum of my mother's and my ages = 40 years.
Now, the ratio of our ages = 4 : 1.
Calculation
Let my age 5 years ago = x years, and my mother's age 5 years ago = y years.
1. x + y = 40
2. Current ages ratio: (y + 5) / (x + 5) = 4 / 1
From equation 1:
y = 40 - x
Substitute y in equation 2:
(40 - x + 5) / (x + 5) = 4 / 1
⇒ (45 - x) / (x + 5) = 4
⇒ 45 - x = 4 × (x + 5)
⇒ 45 - x = 4x + 20
⇒ 45 - 20 = 4x + x
⇒ 25 = 5x
⇒ x = 25 / 5
⇒ x = 5
Now, y = 40 - x
⇒ y = 40 - 5
⇒ y = 35
Current age of my mother = y + 5
⇒ 35 + 5 = 40
My mother's current age is 40 years.
Last updated on Jun 23, 2025
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