Question

Three years ago the ratio of the ages of a and b was 4:3 . three years hence the ratio of their ages will be 11:9 . find the present ages of a and b.

Answer 1

Answer:

Walking along, Tintin overheard the two island gate guards, Thomson and Thompson chatting amongst themselves.

Thomson : He told us we have consecutive letters on our papers

Thompson : Yeah he told me too.

Thomson : I don't know what your letter is.

Thompson : Neither do I know your letter.

Thomson : Now I know.

Tintin listened this conversation and wondered what the two letters could be. When he was

about to leave the island, Thomson stopped him and told him to say the password, which

were the two letters.

Maximum of how many attempts does Tintin need to make to have the correct pair of

letters, and thus pass successfully?

Step-by-step explanation:

Answer 2

Question:

Three years ago, the ratio of the ages of A and B was 4:3. Three years hence, the ratio of their ages will be 11:9. Find the present ages of A and B.

Answer:

A's present age = 19 years

B's present age = 15 years

Solution:

Let the present age of A be x years and the present age of B be y years .

Then , three years ago ;

A's age = (x-3) years

B's age = (y-3) years

Also, three years hence ;

A's age = (x+3) years

B's age = (y+3) years

According to the question;

Three years ago, the ratio of the ages of A and B was 4:3.

Thus;

=> (x-3):(y-3) = 4:3

=> (x-3)/(y-3) = 4/3

=> 3•(x-3) = 4•(y-3)

=> 3x - 9 = 4y - 12

=> 3x - 4y = 9 - 12

=> 3x - 4y = - 3 --------(1)

Also;

Three years hence, the ratio of ages of A and B will be 11:9.

Thus;

=> (x+3):(y+3) = 11:9

=> 9•(x+3) = 11•(y+3)

=> 9x + 27 = 11y + 33

=> 9x - 11y = 33 - 27

=> 9x - 11y = 6 ---------(2)

Now,

Multiplying both sides of eq-(1) , we get;

=> 3•(3x - 4y) = 3•(- 3)

=> 9x - 12y = - 9 ---------(3)

Now,

Subtracting eq-(3) from eq-(2) , we get;

=> (9x - 11y) - (9x - 12y) = 6 - (- 9)

=> 9x - 11y - 9x + 12y = 6 + 9

=> y = 15

Now,

Putting y = 15 in eq-(1) , we get;

=> 3x - 4y = - 3

=> 3x = 4y - 3

=> 3x = 4•15 - 3

=> 3x = 60 - 3

=> 3x = 57

=> x = 57/3

=> x = 19

Hence,

A's present age = x years = 19 years

B's present age = y years = 15 years