in two digit number product of digit is twice the sum of digit then number is
Answers
Step-by-step explanation:
Maths
A two digit number is four times the sum and twice the product of its digits. Find the number.
Asked on December 27, 2019 byavatar
Bhagya Kesarwani
ANSWER
Let no. digit be x and the original no. be 10 x + yx+y
10x + y = 4\left( {x + y} \right)10x+y=4(x+y)
10x + y - 4x - 4y = 010x+y−4x−4y=0
6x - 3y = 06x−3y=0
2x - y = 02x−y=0
2x = y2x=y
Also,
10x + y = 2\left( {xy} \right)10x+y=2(xy)
10x + 2x = 2\left( {2x.x} \right)10x+2x=2(2x.x)
12x = 4{x^2}12x=4x
2
\boxed{x = 3}
x=3
When x = 3,y = 6x=3,y=6
Number is = 36
Answer:
If we represent the number as AB, then it can be expressed mathematically as 10A+B. Since we are looking to find which combination of A and B is twice their product we set that equal to 2AB, ie 10A+B=2AB. Subtract over the 10A and we have 2AB-10A=B. Divide out the A to get A(2B-10)=B. Then divide by (2B-10) and we have A=B/(2B-10), which is useful because it tells us which value A is needed for any given B to meet the requirements that twice the product of the digits is our number. From there simply plug in values for B until A is a positive integer:
B=1, A=-1/8
B=2, A=-1/3
B=3, A=-3/4
B=4, A=-2
B=5, A is indeterminate (5/0)
B=6, A=3
Bingo; our number is 36.
Just for the sake of completeness let's check the rest, just in case there's more than one:
B=7, A=7/4
B=8, A=4/3
B=9, A=9/8
B=0, A=0
Look like there is another, although something tells me you weren't looking for 00.