Question

17. A two-digit number is one more than six times the sum
of its digits and also five more than forty six times the
difference of its digits. Find the number.
(A) 79 B 97 (C) 49 (D) 94​

Answer 1

Step-by-step explanation:

two digit number= 10a+b

case1

10a+b=6(a+b)+1

case2

10a+b=46(a-b)+5

From case1 and 2

=>6(a+b)+1=46(a-b)+5

=>6a+6b=46a-46b+5-1

=>46b+6b=46a-6a+4

=>52b=40a+4

=>40a-52b+4=0

From here factorsize it and find one value

then put that value in any case to find value of other digit.

hope this would help you

Answer 2

Answer:

B) 97

Step-by-step explanation:

Let xy be the 2-digit number, value of number is 10x+y.

first case : 10x+y = 1+6(x+y)

         -->  10x+y = 1+6x+6y

         -->  4x - 5y =1 -----(1)

Second case :  10x+y = 5+46(x-y)

         -->  10x+y = 5+46x-46y

         -->  36x - 47y = 5 -----(2)

By solving eqn (1) & (2)

y =7

now put value of y in eqn (1)

4x - 35 = 1

4x = 36

x = 36/4 = 9

So the number is 97