Question 140

The difference between a two digit number and the number obtained by interchanging the two digits of the number is 9. If the sum of the two digits of the number is 15, then what is the original number?

Solution

Let the unit's digit of the number = $$y$$ and ten's digit = $$x$$

=> Number = $$10x+y$$

Sum of digits = $$x+y=15$$ ----------(i)

According to ques, => $$(10x+y)-(10y+x)=9$$

=> $$9x-9y=9$$

=> $$x-y=1$$ ----------(ii)

Adding equations (i) and (ii), => $$2x=15+1=16$$

=> $$x=\frac{16}{2}=8$$

Substituting it in equation (i), => $$y=15-8=7$$

$$\therefore$$ Original number = 87

=> Ans - (C)

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