14. 2 years ago ‘X’ was 5 times of the age of ‘Y’. Three years later ‘X’ will be three times of ‘Y’. find the present ages.
Answers
❏ Question
2 years ago ‘X’ was 5 times of the age of ‘Y’. Three years later ‘X’ will be three times of ‘Y’. find the present ages.
❏ Solution
Given:-
- 2 years ago ‘X’ was 5 times of the age of ‘Y
- Three years later ‘X’ will be three times of ‘Y’.
Find:-
- present ages of x and y
❏ Explanation
A/c to question ,
(2 years ago ‘X’ was 5 times of the age of ‘Y)
➥ (x-2) = 5.(y-2)
➥x - 5y = -10 +2
➥ x - 5y = -8 ............(1)
And,
( Three years later ‘X’ will be three times of ‘Y’ )
➥ ( x + 3) = 3.(y+3)
➥ x - 3y = 9 - 3
➥ x - 3y = 6 .............(2)
Subtract equ(1) by equ(2).
➥ (-5y + 3y) = -8 - 6
➥ -2y = -14
➥ y = -14/(-2)
➥y = 7
Keep value of y in equ(1),
➥x - 5×7 = -8
➥ x = -8 + 35
➥ x = 27
Thus:-
- Present age of x = 27 years
- present age of y = 7 years.
❏ Verification
Case(1):-
(2 years ago ‘X’ was 5 times of the age of ‘Y)
➥(x-2) = 5.(y-2)
keep value of x and y .
➥ (27-2) = 5.(7-2)
➥ 25 = 5 × 5
➥ 25 = 25
L.H.S = R.H.S
case(2):-
( Three years later ‘X’ will be three times of ‘Y’ )
➥ (x+3) = 3(y+3)
keep value of x and y
➥ (27+3) = 3.(7+3)
➥ 30 = 3 × 10
➥ 30 = 30
L.H.S. = R.H.S
Both cases are proved ,
So, we can say that our solution is right .
⠀⠀⠀⠀ ⠀ ☛...Given...☚⠀⠀ ⠀⠀
✰✰ 2 years ago "X" was 5 times if the age of the age of "Y"...
✰✰ Three years later "X" will be three times of "Y"...
⠀⠀⠀ ⠀ ☛...To find...☚⠀⠀
✰✰ ⠀The present ages of "X" and "Y"...
⠀⠀⠀⠀⠀ ☛...Solution...☚⠀⠀
In case 1st...
2 years ago "X" was 5 times of the age of "Y"...
According to question...
- ☛ X - 2 = 5 ( Y - 2 )
- ✂ X - 2 = 5Y - 10
- ✂ X - 5Y = - 10 + 2
- ✂ X - 5Y = -8 ________ eq 1...
In case 2nd...⠀
Three years later "X" will be three times of "Y"...
According to question...
- ☛ X + 3 = 3 ( Y + 3 )
- ✂ X + 3 = 3Y + 9
- ✂ X - 3Y = 9 - 3
- ✂ X - 3Y = 6 _________ eq 2...
From equation 1st and 2nd...
⠀⠀⠀X - 5Y = - 8
⠀⠀⠀X - 3Y = 6
⠀ ⠀ -⠀+⠀ ⠀-
⠀⠀____________
⠀⠀⠀⠀ - 2Y = - 14⠀ ⠀
⠀ _____________
- ⠀⠀2Y = 14
- ⠀⠀Y = 14 / 2
- ⠀⠀ Y = 7...
Substuting value of "Y" in equation 1...to find the value of "X"...⠀ ⠀⠀
- ⠀⠀X - 5Y = - 8
- ⠀ ⠀X - 5 (7) = - 8
- ⠀⠀ X - 35 = - 8
- ⠀ X = - 8 + 35
- ⠀⠀ X = 27...
Therefore, the present "X" will be 27 years and the present age of "Y" will be 7 years...⠀⠀⠀