Question

The sum of the digits of a two digit number is 9. When the digits are reversed the new number is 9 less than three times the original.

(FOR CLASS 7)​

Answer 1

Answer:

Number is 45.

Explaination:

The sum of two digits of a two digit number is 9. If the digits are interchanged, the new number formed is 9 more than the original number. What is the number?

Let the unit place be ‘x'

Tenth place be y

The number is 10y+x

x+y = 9 (according to the condition) (1)

Digits are interchanged Unit place' y ‘& tenth place ‘ x'

New no is 10x +y

This is 9 more than the original number

10x+ y = 10y+x +9

10x-x+y-10y = 9

9x-9y= 9

x-y = 1 (dividing by 9) (2)

Adding the two equations

2x = 10

x= 5

Substituting the value of x in first equation

y = 4

The number is 45, the original number is 54 this is 9 more of the new number.

Ans :45

Let the two digit number is represented by xy.

Given x + y = 9 when the digits are reversed we get yx. Now yx can also be written as 10y + x since y corresponds to 10 th place and x corresponds to unit place.

xy = 10x + y

given 10y + x -10x -y = 9 => - 9x +9y = 9

= > -x + y = 1. We also know x + y = 9

solving the above equations we get x = 4 and y = 5

=> the number is 45 which when reversed become 54 that is increased by 9.

Hence the digit is 45.

The number is 45.

a+b=9⟹b=9−a

10b+a=10a+b+9

⟹9b=9a+9

⟹b=a+1

⟹a+1=9−a

⟹2a=8

a=4⟹b=5

⟹10a+b⟹40+5=45

Verify:

4+5=9✓

54−45=9✓

Thus verified, the number is 45.

Answer 2

Answer:

Number is 27.

Explanation:

Let the unit digit be x and tens digit be y

then x + y = 9

and number is x + 10y

On reversing the digits it will become 10x + y

As 10x + y is 9

less than three times

x + 10y, we have

10x + y = 3 (x + 10y) − 9

or

10x + y = 3 x + 30y − 9

or

7x − 29y = −9

Multiplying (1) by 29

and adding to (2), we get

36x = 9× 29 − 9 = 9 × 28

or

x = 9 × 28 36 = 7

and hence

y = 9 − 7 = 2

and number is 27 .