The difference of the present ages of two friends Gopal and Manoj is 2 years. If the ratio of their ages after 18 years from now will be 21 : 22, then find the sum of their respective ages 10 years ago from now (in years).
30
Let Gopal's present age be \(G\) and Manoj's present age be \(M\), with \(M - G = 2\).
After 18 years, \(\dfrac{G + 18}{M + 18} = \dfrac{21}{22}\).
Cross-multiplying: \(22(G + 18) = 21(M + 18)\), so \(22G + 396 = 21M + 378\).
This gives \(22G - 21M = -18\). Substituting \(M = G + 2\): \(22G - 21(G + 2) = -18\).
\(22G - 21G - 42 = -18 \Rightarrow G = 24\), and \(M = 26\).
Ages 10 years ago: \(24 - 10 = 14\) and \(26 - 10 = 16\); their sum is \(14 + 16 = 30\).
Hence, the sum of their ages 10 years ago is 30 years.
Similar Questions
The sum of the present ages of two sisters is 67 years. Five years ago from now, the elder sister was twice as old as the younger one. Find the elder sister's current age.
A person is 5 years older than twice their sibling's age. If the person is currently 27 years old, how old is the sibling?
A mother's age is double her son's age at present. If the difference of their ages after 24 years from now is 20, then find their ages at present (in years), respectively.
Important Questions from Age
In 2002, Meenu's age was one-third of the age of Meera, whereas in 2010, Meenu's age was half the age of Meera. What is Meenu's year of birth?
A watch loses 2 minutes in every 24 while another watch gains 2 minutes, in 24 hours. At a particular instant, the two watches showed an identical time. Which of the following statements is correct if 24- hour clock is
The sum of the ages of 5 members comprising a family, 3 years ago was 80 years. The average age of the family today is the same as it was 3 years ago, because of an addition of a baby during the intervening period. How old is the baby ?
5 years ago, my sister's age was 5 times my age. Now it is 3 times only. What is my sister's present age (in years)?
The sum of ages of a father and his son is 45 years. Five years ago, the product of their ages (in yrs.) was 124. The present age of father is :
