Question

The tens digit of a two-digit number is twice the units digits. If the digits are reversed, the new number is 18 less than the original number. Find the number.

Answer 1

✬ Number = 42 ✬

Step-by-step explanation:

Given:

• Tens digit of a two digit number is twice the units digit.
• After reversing digits new number formed is 18 less than original.

To Find:

• What is the number ?

Solution: Let the units digit be x and tens digit be y.

[ Original Number is 10y + x ]

➼ Also tens digit is twice the unit digit.

➼ y = 2x.....(1)

Now the reversing the digit , the new formed is

[ New number = 10x + y ]

A/q

• new number formed is 18 less than original.

$\implies{\rm }$ 10x + y = 10y + x – 18

$\implies{\rm }$ y – 10y = x – 10x – 18

$\implies{\rm }$ – 9y = – 9x – 18

$\implies{\rm }$ –9(2x) = – 9x – 18

$\implies{\rm }$ – 18x = – 9x – 18

$\implies{\rm }$ – 18x + 9x = – 18

$\implies{\rm }$ – 9x = – 18

$\implies{\rm }$ 9x = 18

$\implies{\rm }$ x = 18/9 = 2

So,

➙ Tens digit or y = 2x = 2(2) = 4

➙ One's digit is x = 2

∴ Original Number = 10y + x

=> 10(4) + 2

=> 40 + 2 = 42