Question

Seven times a two digit number is equal to four
times the number obtained by reversing the place of
ots digits. If the difference beyween the digits is 3,
find the number.​

Answer 1

The number is 36

Step-by-step explanation:

Let the tens and units digit of the number be x and y respectively.

According to the 1st condition,

$7(10x + y) = 4(10y + x)$

$70x+7y=40y+4x\\\\70x-4x+7y-40y=0\\\\66x-33y=0 \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, (i)$

According to the 2nd condition,

$x-y=3\\\\x=3+y\, \, \, \, \, \, \, \, \, \, \, \, \, \, (ii)$

Putting the value of x from the equation (ii) in equation (i), we get

$\Rightarrow (3+y)\times 66-33y=0\\\\\Rightarrow 66\times 3+66y-33y=0\\\\\Rightarrow 33y=66\times 3\\\\\Rightarrow y=\frac{66\times 3}{33}=2\times 3\\\\Therefore, y = 6$

Putting the value of y in equation (ii), we get

Not: we can not use the equation (i) because we do not know, which one is greater x or y.

$66x=33y\\\\x=\frac{33\times6}{66} \\\\\\Therefore, x = 3$

Thus, the number is 36.

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Answer 2

plz refer to this attachment