1. Examples
1. At present, ratio of Father's age and Son's age is `6:1`. 5 years hence, ratio of Father's age and Son's age will be `7:2`. At present, Father's age and Son's age is `` ?
Solution:
At present, ratio of Father's age and Son's age is `6:1` (given)
Let their ages be `6x` and `x` years
5 years hence, ratio of Father's age and Son's age will be `7:2` (given)
5 years hence, their ages be `6x+5` and `x+5`
`:.(6x+5)/(x+5)=7/2`
`:.2(6x+5)=7(x+5)`
`:.12x+10=7x+35`
`:.12x-7x=35-10`
`:.5x=25`
`:.x=5`
`:.` Father's present age`=6x=30` years and Son's present age`=x=5` years
2. 2 years ago, Father was `6` times as old as Son. 18 years hence, Father will be `2` times as old as Son. At present, Father's age and Son's age is `` ?
Solution:
2 years ago, Father was `6` times as old as Son (given)
Let 2 years ago Son's age = `x`. Then, 2 years ago Father's age = `6x`.
18 years hence, Father will be `2` times as old as Son (given)
18 years hence, their ages be `6x+20` and `x+20`
`:.6x+20=2(x+20)`
`:.6x+20=2x+40`
`:.6x-2x=40-20`
`:.4x=20`
`:.x=5`
`:.` Father's present age`=6x+2=32` years and Son's present age`=x+2=7` years
This material is intended as a summary. Use your textbook for detail explanation.
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