Question

The sum of the two digit number is 11. The number obtained by adding 4 to this number is 41 less than the reversed number. Find the original number​

Answer 1

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✬ Original Number = 38 ✬

Correct Question: The sum of the digits of a 2-digit number is 11. The number obtained by adding 4 to this number is 41 less than the reversed number. Find the original number.

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Given:

Sum of two digits number is 11.

Number obtained by adding 4 to original number is 41 less than reversed.

To Find:

What is the original number ?

Sooution: Let tens digit be x and ones be y. Therefore original number will be 10x + y.

➟$\bold{Tens + Ones = 11}$

➟$\bold{x + y = 11}$

➟$\bold{x = 11 – y.....(1)}$

[ Now reversed number formed is ]

Reversed number = 10y + x

A/q

Number obtained by adding 4 to original number is 41 less than reversed number.

$\implies{\rm }$$\bold{ 10x + y + 4 = 10y + x – 41}$

$\implies{\rm }$$\bold{10x – x + y – 10y = – 41 – 4}$

$\implies{\rm }$ $\bold{9x – 9y = – 45}$

$\implies{\rm }$$\bold{9(x – y) = – 45}$

$\implies{\rm }$ $\bold{x – y = – 5}$

$\implies{\rm }$$\bold{11 – y = – 5 + y}$

$\implies{\rm }$ $\bold{11 + 5 = y + y}$

$\implies{\rm }$$\bold{16 = 2y}$

$\implies{\rm }$ $\bold{8 = y}$

So, the digits of number are

➭ $\bold{One's digit is y = 8}$

➭ $\bold{Tens digit is x = 11 – 8 = 3}$

Hence, the original number is :-$\bold{ 10x + y = 10(3) + 8 = 38}$

$\large\red{\underline{{\boxed{\textbf{so the original number is = 38}}}}}$

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