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:
A. 18
B. 24
C. 42
D. 81
Answer: Option B
Solution(By Examveda Team)
Let the ten's and unit digit be x and $$\frac{8}{x}$$ respectively$$\eqalign{ & {\text{Then,}} \cr & \left( {10x + \frac{8}{x}} \right) + 18 = 10 \times \frac{8}{x} + x \cr & \Rightarrow 10{x^2} + 8 + 18x = 80 + {x^2} \cr & \Rightarrow 9{x^2} + 18x - 72 = 0 \cr & \Rightarrow {x^2} + 2x - 8 = 0 \cr & \Rightarrow \left( {x + 4} \right)\left( {x - 2} \right) = 0 \cr & \Rightarrow x = 2 \cr} $$
∴ first digit will be 2 and second digit will be 4.
i.e digit is 24.
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Related Questions on Problems on Numbers
If one-third of one-fourth of a number is 15, then three-tenth of that number is:
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C. 45
D. 54
E. None of these
A. 9
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A. 3
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D. Cannot be determined
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Unit digit 8/2=4