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Q.

A two-digit number is such that the product of its digits is 14. If 45 is added to the number, the digits interchange their places. The number is ____.


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Detailed Solution

A two-digit number is such that the product of its digits is 14. If 45 is added to the number, the digits interchange their places. The number is 27.
Given that, a two-digit number is such that the product of its digits is 14.
Let’s assume that the digit at units and tens place is a and b respectively
Then,
a×b=14 b=14a After adding 45 the digits interchange their places,
10b+a+45=10a+b
10b-b+a-10a+45=0
9b-9a-45=0
b-a-5=0
14a-a-5-0
14-a2-5a=0
a2+5a-14=0
a2+7a-2a-14=0
aa+7-2a+7=0
a-2a+7=0
a-2=0 or a+7=0
 a=2 or a=-7
 a=2 Then,   b=14a=142=7 Therefore, the two digits are 2 & 7 and the required number is 27.
 
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