Question

the sum of the digits of a 2 digits of a number is 7 the number obtain by interchanging the digit exect the original number by 27. find the number

Answer 1

Answer:

Step-by-step explanation:

let digit at ones place=x and  

digit at tens place=y

So, the number will be 10y+x

x+y=7 ....(1)

reverse digit will be represented as, 10x+y

So,

(10x+y)-(10y-x)=27

9x-9y=27

x-y=3 ....(2)

Adding equation (1) and (2)

2x=10

x=5

substituting in equation (1)

y=7-5

=2

Thus, the number will be 25

Hope it helps you Mate!

Answer 2

Given

The sum of the digits of a 2 digits of a number is 7 the number obtain by interchanging the digit exceeds the original number by 27.

Find out

Find the number.

Solution

★Let the tens place be x and ones be y

• Original number = (10x + y)

According to the given condition

✰ Sum of the digits of a 2 digits of a number is 7.

• x + y = 7 ----(i)

✰ Number obtain by interchanging the digit exceeds the original number by 27.

• Interchanged number = (10y + x)

➞ 10x + y + 27 = 10y + x

➞ 10x - x + y - 10y = - 27

➞ 9x - 9y = - 27

➞ 9(x - y) = - 27

➞ x - y = - 3 ----(ii)

Add both the equations

➞ (x + y)+(x - y) = 7 - 3

➞ x + y + x - y = 4

➞ 2x = 4

➞ x = 2

Putting the value of x in equation (ii)

➞ x - y = - 3

➞ 2 - y = - 3

➞ y = 3 + 2 = 5

Hence,

• Original number = 10x + y = 25
• Interchanged number= 10y + x= 52

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