Question

two years ago Sunil was four times as old as his son and two years hence twice his age will be equal to 6 times that of his son then the present age of Sunil​

Answer 1

Question:-

two years ago Sunil was four times as old as his son and two years hence twice his age will be equal to 6 times that of his son then the present age of Sunil.

Solution:

Let:

• The present age of Sunil be X
• The present age of his son be Y

To Find:

• Find the present age of Sunil

2 years ago,Sunil was 4 time as old as his son

$\sf{\dashrightarrow X-2=4(Y-2)}$

$\sf{\dashrightarrow X-2=4Y-8}$

$\sf{\dashrightarrow X-4Y=-8+2}$

$\sf{\dashrightarrow X-4Y=-6-----(i)}$

Two years hence twice the age of man will be 6 time as old as his son ,so

$\sf{\dashrightarrow 2(X+2)=6(Y+2)}$

$\sf{\dashrightarrow 2X+4=6Y+12}$

$\sf{\dashrightarrow 2X-6Y=12-4}$

$\sf{\dashrightarrow 2X-6Y=8}$

• Dividing by 2 on both sides

$\sf{\dashrightarrow X-3Y=4----(ii)}$

• Now, Solving equation i and ii here

$\sf{\dashrightarrow X-4Y=-6}$

$\sf{\dashrightarrow X-3Y=4}$

• after solving we get,

$\sf{\dashrightarrow Y=10}$

• Putting the value of Y=10 in EQ (i)

$\sf{\dashrightarrow X-4Y=-6}$

$\sf{\dashrightarrow X-4(10)=-6}$

$\sf{\dashrightarrow X-40=-6}$

$\sf{\dashrightarrow X=-6+40}$

$\sf{\dashrightarrow X=34}$

Hence,

• The present age of Sunil=34 year's

Answer 2

$\mathtt{\huge{ \fbox{Solution :)}}}$

Let ,

The present age of sunil and his son be x and y

Condition I

2 years ago , the age of Sunil was four times as old as his son

Thus ,

➡(x - 2) = 4(y - 2)

➡x - 2 = 4y - 8

➡x - 4y = -6 ----- (i)

Condition II

After 2 years , the twice age of Sunil will be equal to 6 times that of his son

Thus ,

➡2(x + 2) = 6(y + 2)

➡2x + 4 = 6y + 12

➡2x - 6y = 8

➡x - 3y = 4 ----- (ii)

Subtract eq (ii) from eq (i), we get

➡x - 4y - (x - 3y) = -6 - 4

➡-4y + 3y = -10

➡-y = -10

➡y = 10

Substitute the value of y = 10 in eq (ii) , we get

➡x - 3(10) = 4

➡x - 30 = 4

➡x = 30 + 4

➡x = 34

Hence , the present age of sunil and his son are 34 and 10

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