Question

4. A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the nur
digits are reversed. Find the number.
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Answer 1

Let the number be xy which can be written as

xy = 10x + y

According to the Question,

4( x + y ) + 3 = 10x + y

=> 4x + 4y - 10x - y + 3 = 0

=> 3y - 6x + 3 = 0

=> 2x - y = 1 ... eq.01

Now according to the second condition,

10x + y + 18 = 10y + x

=> 9x - 9y + 18 = 0

=> x - y + 2 = 0

=> y - x = 2 ... eq.02

Now we will solve both the Equations by using substitution method.

y = 2x - 1 (from eq. 01)

Putting this value in Eq.02

y - x = 2

=> 2x - 1 - x = 2

=> x - 1 = 2

=> x = 3

Putting this value in equation 01,

2x - y = 1

=> 2 × 3 - y = 1

=> 6 - y = 1

=> - y = -5

=> y = 5

Therefore the number is 35 (ANS)

VERIFICATION :-

Putting both the values in Equation 02,

LHS

= y - x

= 5 - 3

= 2

= RHS

HENCE, LHS = RHS our ANSWER is correct.