Question

When a two-digit number is multiplied by the sum of
its digits, the product is 913. When the number
obtained by interchanging its digits is multiplied by
the sum of the digits, the result is 418. The
difference of the digits of the given number is:​

Answer 1

Step-by-step explanation:

Let the two number be a b .

According to the statement,

(10a+b) * (a+b) = 913

(10b+a) * (a+b) = 413

Solving these two statements,

10a+b/10b+a = 913/418

10a+b/10b+a = 83/38

Now, 83 is prime number cannot be divided further. 83 will be the number . sum will be 11 .

83*11 = 913

38*11 = 418

so sum of digits od 38 = 3+8 = ans is 11

83

apply conditions

(10a+b)*(a+b)=913 ---(1)

(a+10b)*(a+b)=418 ---(2)

divide (1)/(2) we get

(10a+b)/(10b+a)=913/418=83/38 ---(3)

==> Just break equation into two

10a+b=83

a+10b=38

solving the above equations we get a=8 , b=3..Hope the answer is 83.

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Answer 2

Answer: a=8  b=3

Step-by-step explanation:

To find : two numbers

Assuming the two number as a b

According to the question,

10a+b=83

a+10b=38

(10a+b) x (a+b) = 913. (equation 1)

(10b+a) x (a+b) = 413. (equation 2)

Solving the two equations i.e. equation 1 and 2 we get

10a+b/10b+a = 913/418

10a+b/10b+a = 83/38

83 is prime number which cannot be divided further. Hence 83 will be the number and subsequent sum will be 11 .

= 83 x 11 = 913

= 38 x 11 = 418

so sum of digits 3 8 = 3+8 = 11

A variable in mathematics is an alphabet or phrase that represents an unknown number, unknown value, or unknown quantity. Variables are very useful in algebraic expressions or algebra. Numbers are represented in algebra by symbols (typically letters). To answer arithmetic problems, you must understand variables and constants. Letters are used to substitute some numbers when a numerical phrase would be too difficult or when it is preferable to generalise rather than utilise particular numbers. They can also be utilised when you know the values for part of the equation but not the others and need to figure them out.

Hence, a=8  b=3

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