This is the Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for ICSE & CBSE Board.

Question Number 16 Exercise 3E of RS Aggarwal Solution

Here A two-digit number is such that the product of its digit is given. if a number is added to the number, the digits interchange their places.

You have to find the number.

# A two-digit number is such that the product of its digits is 35. If 18 is added to the number, the digits interchange their places. Find the number.

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Let the unit digit be ‘x’

Let the ten’s digit be ‘y’.

Original number will be

10x ten’s digit+ one’s digit

=10x+y

On interchanging of digits,

Let unit’s digit be ‘y’.

Let ten’s digit be ‘x’.

New number will be

10 x ten’s digit + one’s digit

=10y+x

According to question,

Product of digit of two digit number = 35

So, it becomes,

xy=35———–1

If we add 18 to the number the new number obtained is number formed by interchange of digits.

10x+y+18=10y+x

10x-x+18=10y-y

9x+18=9y

18=9(y-x)

18/9=y-x

2=y-x

y=2+x—————2

Put the value of eq(2) in Eq(1).

xy=21

x(2+x)=35

x^2+2x=35

x^2+2x-35=0

x^2+7x-5x-35=0

x(x+7)-5(x+7)=0

(x+7)(x-5)=0

x+7=0

x-5=0

x=-7 ,x=5

x=-7 will be rejected.

So, x=5 and

xy=35

5y=35

y=35/5

y=7

Hence, original number will be

10x+y=10×5+7=50+7=57

New number will be

10y+x=10×7+5=70+5=75

Therefore, Numbers are 57 and 75.