Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q12

Rahim's age is 2/9 of his grandfather's. His grandfather will be 100 years old in 19 years' time. In how many years' time will Rahim's age be 1/4 of his grandfather?

Solution

Now
Rahim --> 2 units
Grandfather --> 9 units

19 years' time (Grandfather)
9 units + 19 --> 100
9 units --> 100 - 19 = 81
1 unit --> 81 divided by 9 = 9

Now
Rahim --> 2 x 9 years = 18 years
Grandfather --> 9 x 9 years = 81 years

Difference between Grandfather and Rahim
--> 81 years - 18 years = 63 years

Future (when Rahim 1/4 of Grandfather's age)
Rahim --> 1 unit
Grandfahter --> 4 units

But Rahim is 63 years younger
4 units - 1 unit --> 63 years
3 units --> 63 years
1 unit --> 63 years divided by 3 = 21 years

Rahim now --> 18 years
Rahim in future --> 21 years

21 years - 18 years = 3 years

Answer: 3 years

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