Question

1.) Two years ago, May was thrice as old as joy. Five years hence, the difference of their ages will be 12. How old is May?

2.) Jay's father is twice as old as Jay. In 20 years, Jay will be two-thirds as old as his father. How old will each be next year?

Answer 1

1) Let the present age of Joy be x years and May's age be y years

ATQ,

2 years ago,

y = 3(x - 2)

➡ y = 3x - 6 -------(i)

And after 5 years,

(y + 5) - (x + 5) = 12

➡ y + 5 - x - 5 = 12

➡ y - x = 12 -------(ii)

Putting value of y from equation (i) in equation (ii)

➡ (3x - 6) - x = 12

➡ 3x - 6 - x = 12

➡ 2x - 6 = 12

➡ x = 18/2

➡ x = 9 years

Putting value of x = 9 in equation (i)

y = 3(9 - 2)

y = 21 years

Hence May is 21 years old.

2) Let the present age of Jay be x years and his father's age be y years.

ATQ,

y = 2x ------(i)

In 20 years,

(x + 20) = 2/3 × (y + 20)

➡ x + 20 = 2/3 (2x + 20) [from equation (i)]

➡ x + 20 = (4x + 40)/3

➡ 3(x + 20) = 4x + 40

➡ 3x + 60 = 4x + 40

➡ 3x - 4x = 40 - 60

➡ x = 20 years

Therefore y = 2x = 40 years

Hence, their age next year will be :-

Jay's = x + 1 = 21 years

Jay's = x + 1 = 21 yearsJay's father's = y + 1 = 41 years

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

1) Two years ago, May was thrice as old as joy. Five years hence, the difference of their ages will be 12. How old is May?

Solution :

Let present age of May be x and of Jay be y.

★ 2 years ago

x = 3(y - 2)

⇒x = 3y - 6.........(1)

★ After 5 years

(x + 5) - (y + 5) = 12

⇒x + 5 - y - 5 = 12

⇒x - y = 12........(2)

Put Value of (1) in (2)

⇒ (3y - 6) - y = 12

⇒3y - 6 -y = 12

⇒2y - 6 = 12

⇒2y = 12 + 6

⇒2y = 18

⇒y = 18/2

⇒y = 9 years

And put Value of y in (2)

⇒x - 9 = 12

⇒x = 12 + 9

⇒x = 21 years

___________________________

★ Age of May = 21 years

★ Age of Jay = 9 years

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2.) Jay's father is twice as old as Jay. In 20 years, Jay will be two-thirds as old as his father. How old will each be next year?

Let age of Jay be x and age of his father be y.

A.T.Q,

y = 2x ......(1)

★ After 20 years

(x + 20) = 2/3 * (y + 20)

Put value of y.

x + 20 = (4x + 40)/3

3(x + 20) = 4x + 40

3x + 60 = 4x + 40

3x - 4x = 40 - 60

-x = -20

x = 20 years

Put Value of x in equation 1.

y = 2(20)

y = 40 years

______________________________

★ Jay's age = x + 1 = 20 + 1 = 21 years

★ Jay's father age = y + 1 = 40 + 1 = 41 years

$\rule{200}{2}$

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