2.
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2. Find the present ages
Five years ago, Jane was ten times as old as her niece and five years hence, three times her age will be equal to twelve times that of her niece.
What is the ratio of their present ages?
Show answer & explanation
Five years ago: J - 5 = 10(N - 5) => J = 10N - 45. Five years hence: 3(J + 5) = 12(N + 5) => J = 4N + 15. Solving gives N = 10, J = 55. Present ratio is 55 : 10 = 11 : 2.
Step-by-step Derivation:
Step 1: J - 5 = 10(N - 5) => J - 5 = 10N - 50 => J = 10N - 45.
Step 2: 3(J + 5) = 12(N + 5) => J + 5 = 4N + 20 => J = 4N + 15.
Step 3: 10N - 45 = 4N + 15 => 6N = 60 => N = 10.
Step 4: J = 4(10) + 15 = 55.
Step 5: Present age ratio J : N = 55 : 10 = 11 : 2.