Newbie

# 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.

• 0

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.

Share

1. 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.

• 0