At the end of 1986 , R was half as old as his grandmother . The sum of the…
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At the end of 1986 , R was half as old as his grandmother . The sum of the years in which they were born is 3846 . How old R was at the end of 1998?
- A.
54
- B.
45
- C.
100
- D.
95
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Correct answer: A
Answer: 54
Let R's age at the end of 1986 be k, so the grandmother's age is 2k.
Their birth years are 1986 - k (for R) and 1986 - 2k (for the grandmother).
The sum of birth years is given as 3846, so (1986 - k) + (1986 - 2k) = 3846.
Simplify: 3972 - 3k = 3846, hence 3k = 126 and k = 42.
R's age at the end of 1998 = 42 + 12 = 54 years.
Therefore, R was 54 years old at the end of 1998.