Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is (M.B.A., 2003)
(a)18
(b)24
(c)42
(d)81
Answer
Answer (as printed): B
Explanation
Let the ten's and unit's digits be $x$ and $\frac{8}{x}$ respectively. Then, $\left(10x+\frac{8}{x}\right)+18=10\times\frac{8}{x}+x \Leftrightarrow 10x^{2}+8+18x=80+x^{2} \Leftrightarrow 9x^{2}+18x-72=0 \Leftrightarrow x^{2}+2x-8=0 \Leftrightarrow (x+4)(x-2)=0 \Leftrightarrow x=2$. So, ten's digit = 2 and unit's digit = 4. Hence, required number $=24$.
Explanation as extracted from the printed page; notation may be imperfect.