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Rashi

· started a discussion

· 1 Months ago

Confusion (Question: 46121.0 )

Can you please explain how we got the RHS in the equation : 10y+x=11y+11x-10x-y

Question:
If a number of two digits is k times the sum of its digits, then the number formed by interchanging the digits is the sum of the digits multiplied by?
Options:
A) 9 + k.
B) 10 + k.
C) 11 – k.
D) k – 1
E) None of these.
Solution:

\(10x+y=K(x+y) \)

\(10y+x=11y+11x-10x-y\)

\(\Rightarrow 10y+x= 11(x+y)-K(x+y)\)

\(\Rightarrow10y+x=(11-k)(x+y)\)


Knowledge Expert

· commented

· 1 Months ago

:)

Rashi

· commented

· 1 Months ago

Thank you!

Knowledge Expert

· commented

· 1 Months ago

why not...



Suppose, we take a two digit number in which x will lie on ten's place and y will lie on unit's place...


So, number = 10x+y


Now if we interchange the places of x and y respectively then we get a new number = 10y+x



Now, its given that,

10x+y = k(x+y)

10x+y=K(x+y)
10y+x=11y+11x−10x−y
⇒10y+x=11(x+y)−K(x+y)
⇒10y+x=(11−k)(x+y)





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