Question

Questions:
1. The sum of the digits of a two-digit no. is 15. the number obtained by interchanging its digits exceeds the given number by 9. Find the original number.

2. The difference between a 2 digit no. and the no. obtained by interchanging its digits is 63. What is the difference between the digits of the no. ?

3. in a3-digit number, the tens digit is thrice the units digit and the hundreds digit is four times the units digit. Also, the sum of its digits is 16. Find the number

Answer 1

1. let the number be 10x + y 

the sum of numbers x+y = 15          -(!)
second , 
10x + y = 10y +x + 9

y - x = 1                                            -(2)

solving both the equations ,
y = 8 and x = 7

2.       let the units digit be b and tens digit be a
then the number is 10a + b
now interchanging the digits is 10b + a

now difference between the numbers are 
10a + b - (10b + a) = 10a + b - 10b - a = 9a-9b

now by factorising,
9(a-b)= 63
a-b = 7

so the difference is 7

3. let us take x as units digit.
then the equation looks like this , 4x + 3x + x = 16 
or 8x = 16
x = 2

therefore , 3x = 3*2 = 6 and 4x = 4 * 2 = 8
so the number is 862