Question

A two-digit numberis 4 times the sum and 3 times the product of its digits. Find the number.​

Answer 1

Answer:24

Step-by-step explanation:

let the two digits be x and y.

Then, the number would be 10x+y (x being in tens place and y in one's place).

According to the quest:-

Case.1-- a two digits number is 4 times the sum of the digits.

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

= 10x-4x=4y-y

= 6x=3y

(÷2) = (2x=y)----- eq.1

According to the quest:-

Case.2-- the number is also equal to 3 times the product of the digits.

10x+y=3xy

Substitute the value of y=2x in place of y.

We get, 10x+2x=(3x)(2x)

= 6x²-12x=0

= 6x(x-2)=0

= 6x=0 so, x=0 or x-2=0 so, x=2.

Consider eq.1:- 2x=y

= 2(2)=y so y=4

OR

= 2(0)=y so y=0

Since we are asked to find out a two digit number. The value of x or y cannot be taking into consideration while its value is 0.

So we take x=2 and y=4

The number:- 10x+y

= 10(2)+4

= 24

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