Question

Q.27 The sum of the digits of a two digit number is 14. If the number formed by
reversing the digits is less than the original number by 18. Find the original
numbers.
orator than 5. If
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Answer 1

Answer:

Step-by-step explanation:

a+b=14------1     10b+a=(10a+b)-18

                         18=9a-9b

                          2=a-b -----------2

therefore,

a+b=14      8+b=14    b=6

a-b=2

2a=16

a=8        

               

Answer 2

Your Answer:

Given:-

• The sum of the digits of a two digit number is 14
• The number formed by reversing the digits is less than the original number by 18.

To Find:-

• The original number.

Solution:-

Let the number at unit digit be y and at the tens place be x

ATQ,

$\tt x+y=14\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow(1)\\\\and\\\\10x+y=10y+x+18\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow(2)$

$\tt Solving\:\:equation\:\:2\\\\ 10x+y=10y+x+18\\\\\Rightarrow 9x-9y=18\\\\\Rightarrow9(x-y)=18\\\\\Rightarrow x-y=2\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow(3)$

Solving equation 1 and 3 we get

x = 8

y = 6

So, the number is

$\blue \tt 10x+y \\\\=10(8)+6\\\\=80+6\\\\=86$