HomeMaths ProblemsThe Ratio between a Two Digit Number and the Sum of the...

# AKIF HAMEED

AUTHOR

If one advances confidently in the direction of his dreams, and endeavors to live the life which he has imagined, he will meet with a success unexpected in common hours.

## Table of Contents – The Ratio between a Two Digit Number | Solution | Problem Solved

• The ratio between a two digit number
• and the sum of the digits of that number is 4 : 1
• The digit is in the unit’s place is 3 more
• than the digit in the ten’s place.
• the required number can be calculate as:

## Important Points to Solve the Problem

Let the unit digit is z and ten’s digit is y.

So, number becomes “10y + z”.

Ratio between a two-digit number (10y + z) and the sum of the digits (y + z) of that number is 4 : 1.

10y + z : y + z = 4 : 1 ________ (i)

Simplification of equation (i) gives

2y = z ________ (ii)

The second condition of the question says

z – 3 = y ________ (iii)

Solving (ii) and (iii) simultaneously we can easily figure out the required number.

Number = ?

## Solution

Let Suppose

Unit digit = z

Ten’s digit = y

Number = 10y + z

According to the first condition of the question

10y + z : y + z = 4 : 1

10y + z = 4 (y + z)

10y + z = 4y + 4z

10y – 4y = 4z – z

6y = 3z

2y = z ________ (i)

According to the second condition of the question

z – 3 = y putting in equation (i)

2 (z – 3) = z

2z – 6 = z

z = 6 and y = 3

Number = 10y + z = 30 + 6 = 36 answer