Question

The sum of a two digit number and the number formed by interchanging the digits is 110.

If 10 is subtracted from the first number, the new number is four more than five times the

sum of the digits in the first number. Find the first number.​

Answer 1

Answer:

64

Solution:

Let the unit place digit be X and tense place digit be y

Then the two digit number will be. 10y+x

And the number formed by interchanging the unit place and tense digit will be 10x+y

According to the first condition given in the qu. I.e, the sum of two numbers is 110

that is

10y+x+10x+y=110

11x+11y=110

divide the above equation by 11 we get

x+y=10

x=10-y......(1)

Now according to the second equation, if 10 is subtracted from the first number that is the number is 10y+x-10

given that the new number is 4more than 5 times the sum of its digit in the first number i.e

the sum it's digit in the in the first number is x+y, now 5 times of its , 5(x+y) , and now 4 more that is , 4+5(x+y)

10y+x-10= 4+5(x+y)

10y-5y+x =4+10+5x

5y=14+4x.....(ii)

substitute the value of x from eq..(I) eq...(ii)

we get

5y=14+4(10-y)

5y=14+40-4y

y=6

and. from eq..I x=4

then the first number 10y+x= 10×6+4=64

First number:64