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Question

A two digit number is such that the product of digits is 16. When 54 is subtracted from the number, the digits interchange their places. Find the number.

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Solution

Let the two digit number =10x+y

It’s digits x and y

Then, according to given question,

x×y=16

y=16x......(1)

Again, according to given question,

10x+y54=10y+x

10x+y10yx54=0

9x9y54=0

xy6=0

xy=6.......(2)

By equation (1) and (2) to, we get,

xy=6

x16x=6

x216=6x

x26x16=0

x2(82)x16=0

x28x+2x16=0

x(x8)+2(x8)=0

(x8)(x+2)=0

x8=0 and x+2=0

x=8 and x=2

Put the value of x in equation (1)

y=16x

y=168=2

But the number is =10x+y

=10×8+2

=82

Hence, this is the number.

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