Question

a two digit no is four times the sum and three time the product of digit find the number find the number

Answer 1

Answer:24

Step-by-step explanation:

let the 10s place digit be x

let the 1s place digit be y

so the number is 10x+y

A.T.P.

10x+y = 4(x+y)----------------------------------------(i)

10x+y = 3xy--------------------------------------------(ii)

FROM (i)

10x+y = 4x+4y

= 6x - 3y = 0----------------------------------------------(iii)

multiplying (iii) with 10 and (ii) with 6

60x - 30y = 0

60x + 6y = 18xy

(-)     (-)       (-)

-----------------------

        -36y = -18 xy

36 y = 18xy

dividing both sides by y

36 = 18 x

x = 2

putting the value of x in (ii)

10 × 2 + y = 3×2×y

20 + y = 6y

y = 6y - 20

y - 6y = -20

-5y = -20

5y = 20

y = 4

so the number = 10 × 2+4

= 24(ans)

Answer 2

Answer:

The required two digit number is 24.

Step-by-step-explanation:

Let the digit at tens place of two digit number be x.

And the digit at units place be y.

Two digit number = xy

⇒ Two digit number = 10x + y

From the first condition,

The two digit number is four times the sum of the digits.

∴ 10x + y = 4 ( x + y )

⇒ 10x + y = 4x + 4y

⇒ 10x - 4x = 4y - y

⇒ 6x = 3y

⇒ 6x / 3 = y

⇒ y = 2x - - - ( 1 )

From the second condition,

The two digit number is three times the product of the digits.

∴ 10x + y = 3xy

⇒ 10x + 2x = 3 x * ( 2x ) - - - [ From ( 1 ) ]

⇒ 12x = 3x * 2x

⇒ 12x = 6x²

⇒ 12 / 6 = x² / x

⇒ 2 = x

⇒ x = 2

By substituting x = 2 in equation ( 1 ), we get,

y = 2x - - - ( 1 )

⇒ y = 2 * 2

⇒ y = 4

Now,

Two digit number = 10x + y

⇒ Two digit number = 10 * 2 + 4

⇒ Two digit number = 20 + 4

⇒ Two digit number = 24

∴ The required two digit number is 24.