Question

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.

Answer 1

❏ 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 .

Answer 2

⠀⠀⠀⠀ ⠀ ☛...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...⠀⠀⠀