25⁶²⁵¹ = 5⁶²⁵¹ = 5 (because unit digit of 5 is always 5)
36⁵²⁸ = 6⁵²⁸ = 6 (because unit digit of 6 is always 6)
73⁵⁴ = 3⁵⁴ = 9(unit digit of 3⁵⁴ = 3² ($$\frac{{54}}{4}$$ = 2 remainder) = 9)
now add all unit digit 5 + 6 + 9 = 20 = 0

Let us assume that he answered x question correctly. Marks scored by him in x question = 4x
Wrong answer would be 200 - x

According to question,
4x - (200 - x) = 200
or 4x - 200 + x = 200
or 5x = 200 + 200 = 400
or x = 80

Let number is N
N is divided by sum of 555 and 445, quotient is 2 times difference
Quotient = 2 (555 - 445) = 220
Remainder = 30 (given)
N = 1000 × 220 + 30
    = 220030

given $${\text{ }}\frac{3}{4}$$ = 0.75     $${\text{ }}\frac{3}{8}$$ = 0.375
(a) $${\text{ }}\frac{7}{9}$$ ? 0.77
(b) $${\text{ }}\frac{7}{3}$$ ? 2.3
(c) $${\text{ }}\frac{5}{9}$$ ? 0.55
(d) $${1\text{ }}\frac{9}{16}$$ = $${\text{ }}\frac{25}{16}$$ ? 1.5
$${\text{ }}\frac{5}{9}$$ = 0.55

$$\eqalign{ & {\text{No}}{\text{. of digits}} \cr & {\text{0 - 9 }} \to {\text{ 1}} \times {\text{9 = 9}} \cr & {\text{10 - 19 }} \to {\text{ 2}} \times {\text{10 = 20}} \cr & {\text{20 - 29 }} \to {\text{ 2}} \times {\text{10 = 20}} \cr & {\text{30 - 39 }} \to {\text{ 2}} \times {\text{10 = 20}} \cr & 40{\text{ - 49 }} \to {\text{ 2}} \times {\text{10 = 20}} \cr & 50\, \to \,2 \times {\text{1 = 2 = 91}} \cr} $$

In this case:
122 (powers of last digit 2 )

2¹ = 2
2² = 4
2³ = 8
2⁴ = 16
2⁵ = 32
2⁶ = 64
2⁷ = 128
2⁸ = 256
2⁹ = 512
??

As you can see, pattern repeats every 4^th power (2, 4, 8, 6).

We have to find 122¹⁷³
Hence, remainder when 173 is divided by 4 = 1
(which corresponds to 1^st number of pattern)
Thus, unit digit of 122¹⁷³ = 2

$$\eqalign{ & {\text{Let number is }}x{\text{}} \cr & {\text{According to question,}} \cr & {\text{3}}\left( {2x + 9} \right) = 75 \cr & 2x + 9 = 25 \cr & x = \frac{{16}}{2} \cr & x = 8 \cr} $$

12345679 × 72
Shortcut method :
Since 72 is factor of 9, So answer should be divisible by 9.
Now check with option by adding digits of option and check which one is divisible by 9.
Here option (c) 888888888 is divisible by 9, so this is multiple of 12345679 × 72

Alternate
12345679 x 72
= 12345679 x (70 +2)
= 12345679 x 70 + 12345679 x 2
= 864197530 + 24691358
= 888888888

$$2.3\overline {49} = \frac{{2349 - 23}}{{990}} = \frac{{2326}}{{990}}$$

Let numerator and denominator br x and 11 - x
According to question,
$$\eqalign{ & {\text{Fraction }} = \frac{x}{{11 - x}} \cr & \Rightarrow \frac{{x + 2}}{{11 - x + 2}} = \frac{x}{{11 - x}} + \frac{1}{{24}} \cr & \Rightarrow \frac{{x + 2}}{{13 - x}} - \frac{x}{{11 - x}} = \frac{1}{{24}} \cr} $$
$$ \Rightarrow \frac{{11x + 22 - {x^2} - 2x - 13x + {x^2}}}{{\left( {13 - x} \right)\left( {11 - x} \right)}}$$       $$ = \frac{1}{{24}}$$
$$\eqalign{ & \Rightarrow \frac{{22 - 4x}}{{143 - 24x + {x^2}}} = \frac{1}{{24}} \cr & \Rightarrow 528 - 96x = 143 - 24x + {x^2} \cr & \Rightarrow {x^2} + 72x - 385 = 0 \cr & \Rightarrow \left( {x + 77} \right)\left( {x - 5} \right) = 0 \cr & \Rightarrow x = 5 \cr & {\text{Numerator }}(x) = 5 \cr & {\text{Denominator }} = 11 - 5 = 6 \cr & {\text{Difference }} = 6 - 5 = 1 \cr} $$