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Question

A two -digit number is such that the product of the digits is 14. When 45 is added to the number, then the digits interchange their places. Find the number.
 


A
72
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B
27
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C
37
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D
14
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Solution

The correct option is C 27
Let the digits be a and b such that the number is 10a+b.
ab =14 and 10a + b+ 45 = 10b + a
i.e., 9a - 9b = -45
i.e., a - b = -5
(a+b)2=(ab)2+4ab=25+4(14)=81a+b=9a=2,b=7
The number is 27.

Quantitative Aptitude

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