Question

A two digit number is four times the sum of the digits it is also equal to 3 time the product of the digits and find the no.

Answer 1

Let the tens place digit be a

and unit place digit be b

According to first condition,

10a + b = 4(a +b)

=> 10a + b = 4a +4b

=> 6a -3b = 0

=> 2a - b = 0

=> b = 2a ---------(1)

Now,

According to second condition ,

3ab = 10a + b

=> 3 a (2a) = 10a + 2a [ using equation 1]

=> 6 a^2 = 12a

=> a = 2

Now,

b = 2×a

=> b= 2 × 2

=> b = 4

Number = 10 (2) + 4

= 20 + 4

= 24

Answer 2

Let the tens place digit be a

and unit place digit be b

According to first condition,

10a + b = 4(a +b)

=> 10a + b = 4a +4b

=> 6a -3b = 0

=> 2a - b = 0

=> b = 2a ---------(1)

Now,

According to second condition ,

3ab = 10a + b

=> 3 a (2a) = 10a + 2a [ using equation 1]

=> 6 a^2 = 12a

=> a = 2

Now,

b = 2×a

=> b= 2 × 2

=> b = 4

Number = 10 (2) + 4

= 20 + 4

= 24