Subject: General Aptitude · Chapter: Problems on Numbers · Exam: 2003 · Marks: · Difficulty:
In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is
(a)24
(b)26
(c)42
(d)46
Answer
Answer (as printed): A
Explanation
Let the ten's digit be $x$. Then, unit's digit $=x+2$. Number $=10 x+(x+2)=11 x+2$; Sum of digits $=x+$ $(x+2)=2 x+2$. $$\begin{aligned} \therefore \quad(11 x+2) & (2 x+2)=144 \\ & \Leftrightarrow 22 x^{2}+26 x-140=0 \\ & \Leftrightarrow 11 x^{2}+13 x-70=0 \\ & \Leftrightarrow(x-2)(11 x+35)=0 \\ & \Leftrightarrow x=2 . \end{aligned}$$ Hence, required number $=11 x+2=24$.
Explanation as extracted from the printed page; notation may be imperfect.