1.

A two-digit number is twice the sum of its two digits. If the two numbers are relocated, then the new number is n times the sum of the two numbers. What is the value of n?

Answer»

Answer:

Let the digit in the ones place be X and TENS place be y

Hence the two digit number =10y+x

GIVEN that the two digit number =4 TIMES sum of its digits

According to the question,

⇒  10y+x=4(x+y)

⇒  10y+x=4x+4y

⇒  3x−6y=0

⇒  x=2y                   ------- ( 1 )

It is also given that the two digit number =2 times product of its digits

⇒  10y+x=2xy

Divide by xy both the sides, we get

⇒  x10+y1=2

Put x=2y from (1), we get

⇒  2y10+y1=2

⇒  y5+y1=2

⇒  y6=2

∴  y=3

⇒  x=2y=2(3)=6

⇒  The two digit number =(10y+x)=10(3)+6=36


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