CDS Model Paper 4 Mathematics

Let the two digit number be 10x+y.
According to the question, 10x+y=3(x+y)
⇒ 10x+y−3x−3y=0
⇒ 7x−2y=0 ...(i)
According to question
⇒ (10x+y)+45=10y+x
⇒ 10x+y+45−10y−x=0
⇒ 9x−9y+45=0
⇒ x−y=−5 ...(ii)
Now, solving equations (i) and (ii), we get
x=2 and y=7
digit =10×2+7=27
∴ sum of the squares of digits =(2)2+(7)2
=4+49=53