Question

Q1- In a two digit number the digit at the units place is thrice the digit in the tens place. The number exceeds the sum of its digits by 27. Find the number .
Q2- A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, its digits are reversed. Find the number. ​

Answer 1

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Answer 2

1)

let 10th digit be x then unit digit is 3x (the digit at the units place is thrice the digit in the tens place)

And the number is 10x+3x

sum of tenth and unit digit =number -27

x+3x=10x+3x-27

27=13x-4x

9x=27

x=3

3x=9

number = 10x +3x

Number is 39

2)let unit digit be y and 10th digit be x

Number is 10x +y

sum of digit

Equation for this

A two digit number is 3 more than 4 times the sum of its digits

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

10x+y=3+4x+4y

6x-3y=3

2x-y=1

y=2x+1 --------Equation (i)

Equation for this

If 18 is added to the number, its digits are reversed

10x+y +18=10y+x

Putting value of y from equation (i)

10x+(2x+1)+18=10 (2x+1)+x

12x+19=20x+10+x

19-10=9x

x=1

y=2x+1

y=2×1+1

y=3

Number is 10x+y

Number is 10+3=13

Number is 13

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