Question

In a three-digit number, the digit in the unit's place is 4 times the digit in the hundred's place. If the digit in the unit's place and ten's place are interchanged, the new number such formed is 18 more than the original number. If the digit in the hundred's place is one-third of the digit in the ten's place, what is 25% of the original number?

Answer 1

The digit in units is four times that of the digit in hundred.

$x \: y \: 4x \: + 18 = x \: 4x \: y$if the numbers in units and tens place are interchanged the new number is 18 more than the original one.

$if \: hundreds \: digit = x \\ units \: digit = 4x$

$if \: hundreds \: digit = \\ 1 \div 3 \times tens \: digit$

$tens \: digit = 3 \times hundred \: digit$

A.T.P,

$x \times 100 + y \times 10 + 4x \times 1 + 18 = \\ x \times 100 + 4x \times 10 + y \times 1$

$100x + 10y + 4x + 18 = \\ 100 x + 40x + y$

$= 10y + 4x + 18 = 40x + y$

$= 10y - y + 18 = 40x - 4x$

$9y + 18 = 36x$

$9y + 36x = 18$

$9(y + 4x) = 18$

$y + 4x = 18 \div 9 =$

$y + 4x = 2$

$= 3 \times 4 \times x = y$

$12x + 4x = 2$

$16x = 2$

$x = 2 \div 16$

$then \\ hundred \: digit = 2 \div 16 = \\ 2 \div 16 =1 \div 8 \\ tens \: digit \: = 3 \times1 \div 8 = 3 \div 8 \\ ones \: digit = 4 \times 2 \div 16 = 2 \div 4 \\ = 1 \div 2$

Therefore the number is

$100 \times 1 \div 8 + 10 \times 3 \div 8 + 1 \div 2 \\ = 12.5 + 3.75 + 0.5 = 16.75$

$25 \div 100 \times 16.75 = 4.1875$

THEREFORE THE ANSWER IS 4.1875

THANK IF USEFUL