Question
In 12 years, the ratio of the
ages of 'Arjuna' and 'Bheem' will be 8:7. Currently, the average of the ages of 'Arjuna' and 'Charu' is 30 years, and 'Bheem's present age is 25% greater than 'Charu's current age. What is the ratio of the current ages of 'Arjuna', 'Charu', and 'Bheem'?Solution
ATQ, Let ages of ‘Arjuna’ and ‘Bheem’, after 12 years will be ‘8x’ years and ‘7x’ years respectively. Let present age of ‘Charu’ is ‘z’ years. So, (8x – 12 + z) = 30 × 2 Or, z = 72 – 8x And, 7x – 12 = 1.25 × z = 1.25 × (72 – 8x) Or, 7x – 12 = 90 – 10x Or, 17x = 102 Or, x = 6 Present age of ‘Arjuna’ = 8 × 6 – 12 = 36 years Present age of ‘Bheem’ = 7 × 6 – 12 = 30 years Present age of ‘Charu’ = 72 – 8 × 6 = 24 years Desired ratio = 36:24:30 = 6:4:5
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