Question
Currently, the combined ages of
'P' and 'Q' add up to 78 years. The ratio of 'P's age 2 years ago to 'Q's age 2 years in the future is 5:8. One year from now, 'P's age will be 10% greater than 'R's age at that time. What is the ratio of 'Q's age 6 years ago to 'R's age 1 year ago?Solution
ATQ, 2 years ago, from now, let the age of 'P' = '5x' years 2 years hence from now, let the age of 'Q' = '8x' years So, sum of present ages of 'P' and 'Q' = 5x + 2 + 8x - 2 = '13x' years Or, 13x = 78 So, x = 78 ÷ 13 = 6 So, present age of 'P' = 5x + 2 = 32 years Present age of 'Q' = 78 - 32 = 46 years 1 year hence from now, age of 'P' = 32 + 1 = 33 years 1 year hence from now, age of 'R' = 33 ÷ 1.1 = 30 years So, present age of 'R' = 30 - 1 = 29 years So, required ratio = (46 - 6):(29 - 1) = 40:28 = 10:7
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