Steps: 1 Mark
Result: 1 Mark
$\frac{2x+1}{3x-2}=\frac{9}{10}$
$\Rightarrow 10(2x+1)=9(3x-2)$
$\Rightarrow 20x+10=27x-18$
$\Rightarrow 10+18=27x-20x$
$\Rightarrow 28=7x$
$\Rightarrow 7x=28$
$\Rightarrow x=\frac{28}{7}=4$
The value of 'x' is 4.

Framing the equation: 1 Mark
Result: 1 Mark
Let the number be y
Then, $3y-10=17$
 $\Rightarrow 3y=17+10$
$\Rightarrow 3y=27$
$\Rightarrow y=9$

Framing the equation: 1 Mark
Steps: 1 Mark
Result: 1 Mark
Let the present age of Gaurav be $x$.
According to question, In 13 years, Gaurav' age $=24$
$\Rightarrow x+13=24$
$\Rightarrow x=11$
The expression for Gaurav's age for 20 years from now = $x+20$
After 20 years, Gaurav's age will be:
$x+20$
$11+20=31years$
Since Gaurav's present age is 11 years
$\therefore$ After 20 years father's age will be = $6\left(11\right)-3=66-3=63$
Hence, father's present age = $63-20=43years$

Each part: 1.5 Mark
a) There are many numbers of equations that satisfy $y=6$
First equation: $4y-8=16$
Second equation: $\frac{7y}{3}-4=10$;
b) There are number of equations that satisfy $y=-8$
First equation: $4y-8=-40$
Second equation: $\frac{7y}{4}+24=10$

Framing the equation: 1 Mark
Steps: 1 Mark
Result: 1 Mark
Let the first number be $9x$
Then, second consecutive number $=9(x+1)$
Third consecutive number $=9(x+2)$,
And, fourth consecutive number $=9(x+3)$
According to question:
$9x+9(x+1)+9(x+2)+9(x+3)=378$
$\Rightarrow 9x+9x+9+9x+18+9x+27=378$
$\Rightarrow 36x+54=378$
$\Rightarrow 36x=378-54$
$\Rightarrow 36x=324$
$\Rightarrow x=\frac{324}{36}=9$
The numbers are 81, 90, 99 and 108.

Each part: 2  Marks
a) Let the number be $y$
According to question, $(y\times 6)+4=54$
$\Rightarrow 6y=54-4$
$\Rightarrow 6y=50$
$\Rightarrow y=\frac{50}{6}$
b) Let the number is $y$;
According to question, $6+4\times y=88$.
$\Rightarrow 6+4y=88$
$\Rightarrow 4y=88-6$
$\Rightarrow 4y=82$
$\Rightarrow y=\frac{82}{4}$

(a) Correct statement of equation: 1 Mark each
(b) Framing of equation: 1 Mark
     Solution: 1 Mark
(a) i) When a number is multiplied with 7 and 4 is added to their product, we get 46 as the final result.
     ii) When a number is multiplied with 5, 4 is added to their product and their final sum is divided by 6, the result which we get is 13.
(b) Let Raju's age be x.
     Raju's father's age = $3x+5=44$
     $\Rightarrow 3x+5=44$
     $\Rightarrow 3x=44-5=39$
     $\Rightarrow x=\frac{39}{3}$
     $\Rightarrow x=13years$
Raju's age is 13 years.

Framing the equation: 1 Mark
Steps: 2 Marks
Result: 1 Mark
Let the numerator of a rational number $=x$
Then the denominator of a rational number $=x+3$
When numerator is increased by 7, then new numerator $=x+7$
When denominator is decreased by 1, then new denominator $=x+3-1$
The new number formed $=\frac{3}{2}$
According to the question,
$\frac{x+7}{x+3-1}=\frac{3}{2}$
$\Rightarrow \frac{x+7}{x+2}=\frac{3}{2}$
$\Rightarrow 2(x+7)=3(x+2)$
$\Rightarrow 2x+14=3x+6$
$\Rightarrow 3x-2x=14-6$
$\Rightarrow x=8$
Numerator = 8, then denominator = 8+3 = 11
Original fraction $=\frac{8}{11}$