Select the correct answerAge of the father is twice that of the elder son. Ten years hence the age of the father will be three times that of the younger son. If the difference of the ages of the two sons is 15 years, the age (in years) of the father is?Options55506070
Question
Select the correct answerAge of the father is twice that of the elder son. Ten years hence the age of the father will be three times that of the younger son. If the difference of the ages of the two sons is 15 years, the age (in years) of the father is?Options55506070
Solution
Let's denote the current age of the elder son as E, the current age of the younger son as Y, and the current age of the father as F.
From the problem, we have the following equations:
-
F = 2E (The age of the father is twice that of the elder son)
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F + 10 = 3(Y + 10) (In ten years, the age of the father will be three times that of the younger son)
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E - Y = 15 (The difference of the ages of the two sons is 15 years)
We can substitute equation 1 into equation 2 to get:
2E + 10 = 3Y + 30
Solving for E, we get:
E = 3Y/2 + 10
Substituting equation 3 into this equation, we get:
15 + Y = 3Y/2 + 10
Multiplying through by 2 to clear the fraction, we get:
30 + 2Y = 3Y + 20
Solving for Y, we get:
Y = 10
Substituting Y = 10 into equation 3, we get:
E = 25
Substituting E = 25 into equation 1, we get:
F = 2 * 25 = 50
So, the father is 50 years old. The correct answer is 50.
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