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Question

# A two digit number in such that the product of its digits is 8. When 63 is subtracted from the number, the digits interchange their places. Find the number.

A
18
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B
72
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C
27
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D
81
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Solution

## The correct option is C 81Let the digit at unit's place =x∴ Digit at ten's place 8x and the number is (80x+x)New number on interchanging the places of digits =10x+8x∴ According to given condition80x+x−63=10x+8x80+x2−63x=10x2+89x2+63x−72=0x2−7x−8=0x2+8x−x−8=0x(x+8)−1(x+8)=0(x+8)(x−1)=0i.e.x=−8 and x=1Rejecting x=−8 and putting x=1 the required no. is (801+1)=81.

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