Question 64
A number lying between 10 and 100 is seven times the sum of digits. If 9 is subtracted from it, the digits of the number are reversed. The number is
Solution
Let the unit's digit is $$y$$ and ten's digit is $$x$$, => Number = $$10x+y$$
=> $$10x+y=7(x+y)$$
=> $$10x+y=7x+7y$$
=> $$3x=6y$$
=> $$x=2y$$ ----------------(i)
Also, $$10x+y-9=10y+x$$
=> $$9(x-y)=9$$
=> $$x-y=1$$
Substituting value from equation (i), => $$2y-y=y=1$$
=> $$x=2$$
$$\therefore$$ Original number = 21
=> Ans - (A)
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