1. Examples
1. At present, ratio of Meena's age and Kamla's age is `3:5`. At present, sum of Meena's age and Kamla's age is `80`. 10 years hence, ratio of Meena's age and Kamla's age will be ``?
Solution:
At present, ratio of Meena's age and Kamla's age is `3:5` (given)
Let their ages be `3x` and `5x` years
At present, sum of Meena's age and Kamla's age is `80` (given)
`:.3x+5x=80`
`:.8x=80`
`:.x=10`
`:.` Meena's present age`=3x=30` years and Kamla's present age`=5x=50` years
`:.` Their ages after 10 years will be `40` and `60` years
`:.` Ratio of their ages `=40:60``=2:3`
`:.` 10 years hence, ratio of Meena's age and Kamla's age will be `2:3`
2. 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
3. 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
4. 10 years ago, a was 4 times as old as b. 10 years hence, a will be 2 times as old as b. at present, a's age and b's age is ?
Solution:
10 years ago, A was `4` times as old as B. (given)
Let 10 years ago B.'s age = `x`. Then, 10 years ago A's age = `4x`.
10 years hence, A will be `2` times as old as B. (given)
10 years hence, their ages be `4x+20` and `x+20`
`:.4x+20=2(x+20)`
`:.4x+20=2x+40`
`:.4x-2x=40-20`
`:.2x=20`
`:.x=10`
`:.` A's present age`=4x+10=50` years and B.'s present age`=x+10=20` years
5. At present, a is 3/5 times as old as b. at present, sum of a's age and b's age is 80. 10 years hence, ratio of a's age and b's age will be ?
Solution:
At present, A is `3/5` times as old as B. (given)
Let B.'s age = `x`. Then, A's age = `(3x)/(5)`.
At present, sum of A's age and B.'s age is `80` (given)
`:.((3x)/(5))+x=80`
`:.(8x)/(5)=80-0`
`:.(8x)/(5)=80`
`:.x=50`
`:.` A's present age`=30` years and B.'s present age`=50` years
`:.` Their ages after 10 years will be `40` and `60` years
`:.` Ratio of their ages `=40:60``=2:3`
`:.` 10 years hence, ratio of A's age and B.'s age will be `2:3`
6. 1 years ago, difference of a's age and b's age was 20. 5 years ago, a was 5 times as old as b. at present, a's age and b's age is ?
Solution:
1 years ago, difference of A's age and B's age was `20` (given)
Let 1 years ago B's age = `x`, then 1 years ago A's age = `x+20`.
5 years ago, A was `5` times as old as B (given)
5 years ago, their ages be `x+16` and `x-4`
`:.x+16=5(x-4)`
`:.x+16=5x-20`
`:.5x-x=20+16`
`:.4x=36`
`:.x=9`
`:.` A's present age`=x+20+1=30` years and B's present age`=x+1=10` years
7. At present, Ram is `2` times as old as Shyam. 10 years ago, Ram was `4` times as old as Shyam. At present, Ram's age and Shyam's age is ``?
Solution:
At present, Ram is `2` times as old as Shyam (given)
Let Shyam's age = `x`. Then, Ram's age = `2x`.
10 years ago, Ram was `4` times as old as Shyam (given)
10 years ago, their ages be `2x-10` and `x-10`
`:.2x-10=4(x-10)`
`:.2x-10=4x-40`
`:.2x-4x=-40+10`
`:.-2x=-30`
`:.x=15`
`:.` Ram's present age`=30` years and Shyam's present age`=15` years
This material is intended as a summary. Use your textbook for detail explanation.
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