Question

A two digit number is four times the sum and three times the product of its digits . Find the number

Answer 1

Let the digits be x and y

Then the two-digit number is 10x + y

Given

10x + y = 4 (x + y)

10x + y = 4x + 4y

6x = 3y

y = 2x ……..1

Given

10x + y = 3xy………….2

Substitute the value of y in eqn 2

10x + 2x = 3x * 2x

12x = 6x2

Dividing both side by x

12 = 6x

x = 2

Therefore, y = 2 * 2

                     y = 4

 

Therefore, the two-digit number = 10x + y = 10 *2 + 4 = 24

Answer 2

Suppose unit digit be p

Tens digit be m

Number = 10m + p

Now

10m + p = 4(p + m)

6m - 3p = 0

2m - p = 0 .......... (1)

Also

10m + p = 3pm

10m + 2m = 3pm ..... (From equation 1)

12m = 3pm

3m (4 - p) = 0

m = 0

p = 4

Avoid 0

p = 4

From equation 1 we get :-

2m - 4 = 0

2m = 4

${\implies m = \dfrac{4}{2}}$

Required Number :-

= 2 × 10 + 4

= 24

Q.E.D