[11 years] In three more years, Miguels grandfather will be six times as old as Miguel was lastyear. When M

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In three more years, Miguels grandfather will be six times as old as Miguel was last
year. When Miguels present age is added to his grandfathers present age, the total is 68.
How old is each one now?

11 years

12 years

10 years

15 years

Explanation:

Miguels present age be "m"
Grandfathers present age be "g"
Then m + g = 68
Miguels age "last year" was m – 1
His grandfathers age "in three more years" will be g + 3
The grandfathers "age three years from now" is six times Miguels "age last year"
i.e., g + 3 = 6(m – 1)
This gives me two equations with two variables:
m + g = 68
g + 3 = 6(m – 1)
Solving the first equation,
m = 68 – g
g + 3 = 6m – 6
g + 3 = 6(68 – g) – 6
g + 3 = 408 – 6g – 6
g + 3 = 402 – 6g
g + 6g = 402 – 3
7g = 399
g = 57
Since "g" stands for the grandfathers current age, then the grandfather is 57.
Since m + g = 68,
then m = 11
Miguel is presently eleven years old

Additional Questions

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One year ago, the ratio of Gauravs and Sachins age was 6: 7 respectively. Four years hence, this ratio would become 7: 8. How old is Sa chin ?	Answer
The Ratio of Ages of Mona and Sona is 4:5. Twelve Years hence, their ages will be in the ratio of 5:6. What will be Sonas age after 6 years ?	Answer
Ramu was 4 times as old as his son 8 years ago. After 8 years, Ramu will be twice as old as his son. What their present ages ?	Answer
A man is four times as old as his son. Five years ago, the man was nine times as old his son was at that time. What is the present age of a man ?	Answer
The sum of ages of Aruna and her mother is 49 years. Also, 7 years ago, the mothers age was 4 times Arunas age. Find the present age of Arunas mother.	Answer
The ages of A and B differ by 16 years. If 6 years ago, the elder one be 3 times as old as the younger one, find their present ages.	Answer
In three more years, Miguels grandfather will be six times as old as Miguel was last year. When Miguels present age is added to his grandfathers present age, the total is 68. How old is each one now?	Answer

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