Question

5 years ago,A was thrice as old as B and 10 years later A shall be twice as old as B . what is percent age of A 20 aur 50 or 60 or 40​

Answer 1

Step-by-step explanation:

Five years ago, A was thrice as old as B

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

Five years ago their ages A's age x - 5 and B's age y - 5

(x - 5) = 3 (y - 5)

x - 5 = 3y - 15

x = 3y - 10….. Eq. 1

Ten years later, A shall be twice as old as B, Thus ten years later their ages will be x + 10 and y + 10

(x +10) = 2 (y + 10)

x + 10 = 2y + 20

x - 2y = 20 - 10

x - 2y = 10…. Eq..2

Substituting value of x from Eq..1 to Eq..2

(3y - 10) - 2y = 10

3y - 2y = 10 + 10

y = 20

The age of B is 20 years

Now substituting the value of y in Eq..2 to derive value of x

x - 2y = 10

x - 2 (20) = 10

x - 40 = 10

x = 10 + 40

x = 50

Thus the age of A is 50 years and age of B is 20 years.The sum of their ages

A + B = 50 + 20 = 70 years

Sum of their ages is 70 years

Answer the age of A is 50 years and age of B is 20 years and sum of their ages is 70 years

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Answer 2

Given :-

• Five years ago,A was thrice as old as B and

• Ten years later A shall be twice as old as B.

To find :-

• Present age of A and B = ?

Solution :-

Let the present age of B be x years

and present age of A be y years.

then,

Case I,

$\bf\dag{\underline{Five\:years\:ago}}:-$

• Age of B = (x - 5) years
• Age of B = (y - 5) years

According to the question,

(y - 5) = 3(x - 5)

⤇ y - 5 = 3x - 15

⤇ -5 + 15 = 3x - y

⤇ 10 = 3x - y

⤇ 3x - y = 10 ..................................(i)

Case II,

$\bf\dag{\underline{Ten\:years\:later}}:-$

• Age of B = (x + 10) years
• Age of A = (y + 10) years

According to the question,

(y + 10) = 2(x + 10)

⤇ y + 10 = 2x + 20

⤇ 10 - 20 = 2x - y

⤇ -10 = 2x - y

⤇ 2x - y = -10 .....................................(ii)

Subtracting eq (ii) from eq (i),

(3x - y) - (2x - y) = 10 - (-10)

⤇ 3x - 2x - y - (-y) = 10 + 10

⤇ x - y + y = 20

⤇ x = 20

putting the value of x in equation (i),

3x - y = 10

⤇ 3 × 20 - y = 10

⤇ 60 - y = 10

⤇ -y = 10 - 60

⤇ -y = - 50

⤇ y = 50

Hence,the present age of B will be 20 years and present age of A will be 50 years.