Question

A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:

Answer 1

the answer is 253
explaination consider x+y+z=10
                                y=x+z
 sub y value in 2x+2z=10
                         x+z=5
                         sub in x+y+z=10
                       5+y=10
                           y=5,x+z=5,then x=2,z=3

Answer 2

Answer:

253

Step-by-step explanation:

Let he the number be xyz

Since we are given that the sum of the digits is 10

So, $x+y+z=10$  ---1

Now we are given that The middle digit is equal to the sum of the other two

So, $y = x+z$  --2

Now we are given that the number will be increased by 99 if its digits are reversed.

⇒$100x+10y+z+99=100z+10y+x$

⇒$100x+z+99=100z+x$

⇒$99x+99=99z$

⇒$x+1=z$

⇒$x=z-1$  --3

Substitute the value of x in 2

$y = z-1+z$

$y =2z-1$

Substitute the value of x and y in 1

$z-1+2z-1+z=10$

$4z-2=10$

$4z=12$

$z=3$

Substitute the value of z in 3

⇒$x=3-1$

⇒$x=2$

Substitute the value of z and x in 1

$2+y+3=10$

[tex]y=5/tex]

Thus the number is xyz=253

Hence the number is 253