Question

The difference between the tom and harry is 6 years. 10years later the product of their ages will be 280. How old are tom and harry now?

Answer 1

ɢɪᴠᴇɴ :-

The difference between the tom and harry is 6 years. 10years later the product of their ages will be 280.

ᴛᴏ ғɪɴᴅ :-

• Tom's age

• Harry's age

Sᴏʟᴜᴛɪᴏɴ :-

➦ Let Tom's age be x years

And,

➦ Harry's age be y years

Then,

➭ ( x - y) = 6

➭ x = (6 + y). --(1)

10 years later,

Tom's age = (x + 10) years

Harry's age = (y + 10) years

Product = xy = 280

➮ (x + 10)(y + 10) = 280.

➮ ( 6 + y + 10)(y + 10) = 280 --(from -1)

➮ (y + 16)(y + 10) = 280

➮ y² + 10y + 16y + 160 = 280

➮ 26y + y² = 280 - 160

➮ y² + 26y - 120 = 0

➮ y² + 30y - 4y - 120 = 0

➮ y( y + 30) - 4( y +30) = 0

➮ ( y - 4) ( y + 30) = 0

➮ y = 4. or y = -30

Hence,

➦ Age can't be negative.

So,

We take y = 4

Put y = 4 in (1) , we get,

➮ x = 6 + y

➮ x = 6 + 4

➮ x = 10

Hence,

Age of :-

✑ Tom = x = 10 years

✑ Harry = y = 4 years

Answer 2

ꜱᴏʟᴜᴛɪᴏɴ :

• Let's Tom's age be x

• Let's Harry's age be y

ACQ :-

➨ x - y = 6

➨ x = y + 6 ------- ( 1 )

10 years later

➨ ( x + 10 ) * ( y + 10 ) = 280

➨ xy + 10x + 10y + 100 = 280

Substitute value of x from ( 1 )

➨ y ( y + 6 ) + 10 ( y + 6 ) + 10y = 280 - 100

➨ y² + 6y + 10y + 60 + 10y = 180

➨ y² + 26y = 180 - 60

➨ y² + 26y = 120

➨ y² + 26y - 120 = 0

By splitting middle term

➨ y² + 30 - 4y - 120 = 0

➨ y ( y + 30 ) - 4 ( y + 30 ) = 0

➨ ( y - 4 ) ( y + 30 ) = 0

y - 4 = 0 y + 30 = 0

y = 4 y = - 30

Age can't be -ve so 4 is right

Age can't be -ve so 4 is right Put value of y in ( 1 ) to find value of x

➨ x = y + 6

➨ x = 4 + 6

x = 10

Tom's age is 10 years and Harry's age is 4 years