Musa is three years older than Manya. Seven years ago, Musa was twice as old as Manya. (1) How old are they now? (2) When will the sum of them be 45?
Question 1 Report
Musa is three years older than Manya. Seven years ago, Musa was twice as old as Manya. (1) How old are they now? (2) When will the sum of them be 45?
Answer Details
Let Manya's present age be \(m\). Then Musa \(= m + 3\).
Seven years ago Musa was twice Manya:
\[(m + 3) - 7 = 2(m - 7)\] \[m - 4 = 2m - 14 \Rightarrow m = 10\](1) Manya is \(10\) years and Musa is \(13\) years now.
(2) The present sum of ages is \(23\), and it rises by 2 each year. Let it take \(t\) years:
\[23 + 2t = 45 \Rightarrow 2t = 22 \Rightarrow t = 11\]The sum of their ages will be 45 in 11 years.
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