Question

1. Find the number which consists of 3 digits and the sum of the three digits 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.

Answer 1

253

Explanation:

Let he the number be xyz

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

So, ---1

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

So, --2

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

⇒

⇒

⇒

⇒

⇒ --3

Substitute the value of x in 2

Substitute the value of x and y in 1

Substitute the value of z in 3

⇒

⇒

Substitute the value of z and x in 1

[tex]y=5/tex]

Thus the number is xyz=253

Hence the number is 253

Answer 2

Explanation:

Let x,y,z be the 3 digits of the no. in that order. It is given, x+y+z =10 …..(1)

y=x+z

Substituting the value of y in 1

x+x+z+z=10

2x+2z=10

x+z=5…….(2)

100x+10y+z+99=100z+10y+x

99x+99=99z

x+1=z…..(3)

Substituting the value z in 2

x+x+1==5

2x=4

x=2

Substituting the value of x in 3

z=3

y=5

Si the no. is 253