As g (x) is reflected about x – axis.

    g(x) = -f(x)

Let, hundred’s digit = x,

Ten’s digit = y and units digit = z

x + y = z + 1 -------------------(1)

x2 + 1 = y -----------------------(2)

x2  + y2  = z2  - 7 ----------------(3)

x + x2  + 1= z + 1

⇒ z = x2 + x

⇒ z2 = x4 + 2x3 + x2---------------(4)

Also, x2 + (x2 +1)2 = x4 + 2x3 + x2 –7 

⇒ 2 x3 - 2 x2 = 8 x3 - x2  - 4 = 0

⇒  (x-2) (x2 + x + 2) = 0

x = 2, (since x2 + x + 2 = 0 gives imaginary roots)

∴ From (2),  y = (2)2 x2

⇒ Z =  x + y – 1 = 2 + 5 – 1 = 6

∴The number is 256   

Note : The best approach here is clearly back substitution from the given answer choices.

Let the price of each apple , banana and orange be C,G and D respectively Given 

C+G=55-------------(1);

G+2D=40 -----------(2)

Week’s purchases are

C + (G+D) + (2G) + (2D) + (C+G+D)

= 2C + 4G + 4D = 2 (C + 2G + 2D)

By adding equations (1) and (2),

We get C + 2G + 2D = 95

Hence, entire week’s purchase = 2 95 = Rs. 190

Here there is no need of framing any equation to solve the problem. After the transfer of marbles first time, since Ram has seven times as many marbles as sam, the total number of marbles with the two of them together will be a multiple of 8. similarly, after the second transfer, Sam has eight times the number of marbles Ram has, the total number of marbles with the two of them together will be a multiple of 9. since the total number of marbles is a multiple of 8 as well as 9, from the answer choices, we have only 72. [The actual numbers are 50 and 22].