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Fill in the blanks:
(i) If Nikita travels 252km in 2 hours, then she travels…P……. km in 21 hours.
(ii) If the cost price of 5 chairs and 6 tables is Rs. 750 and Rs. 3600 respectively, then the cost price of 3
      such chairs and 2 such tables in Rs. …………..Q……….
(iii) The ratio of the number of boys to total number of students in a class is ….R……….. , if the number of
        boys and girls are 36 and 18 respectively.

A. (i)400 (ii)1680 (iii)2:3
B. (i)400 (ii)1650 (iii)2:3
C. (I)441 (ii)1650 (iii)2:3
D. (i)441 (ii)1680 (iii)2:3

Answer
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Hint: For all the statements given in the question, we will use the unitary method approach to find the answers and fill the blanks by calculating different quantities P,Q and R- distance, cost and ratio respectively .

Complete step-by-step answer: Now, in this question, every part of the question represents a different scenario.
So, starting with the first statement:
(i) Given, that Nikita travels 252 km in 12 hours,
Then, using a unitary method, first we will evaluate the distance travelled in 1 hour.
So, Distance travelled by Nikita in 12 hours $ = 252km$
Then, distance travelled by Nikita in 1 hour will be lesser, that is $ = \dfrac{{252}}{{12}} = 21km$
Therefore, the distance travelled by Nikita in 21 hours will be certainly more than the distance travelled in 1 hour, so we will multiply the distance travelled in the above step with 21 to get the answer = $21 \times 21 = 441km$ .
So,$P = 441$ will be put in the first blank.

(ii) According to the question:
Cost of 5 chairs is Rs. 750, and cost of 6 tables is Rs. 3600. To find the cost of 3 such chairs and 2 such tables, we need to find the cost of one table and one chair first, using unitary method,
So, if the cost of 5 chairs is Rs. 750,
Then, the cost of 1 chair will be$Rs.\dfrac{{750}}{5} = Rs.150$,
Therefore, the cost of 3 chairs will be$ = Rs.150 \times 3 = Rs.450$ .
Next, if cost of 6 tables is Rs. 3600,
Then cost of 1 table will be $Rs.\dfrac{{3600}}{6} = Rs.600$
Therefore, the cost of 2 tables = $ = Rs.600 \times 2 = Rs.1200$.
Hence, to find the cost of 3 chairs and 2 tables we will add their collective prices and find the total sum.
So Q = Cost of 3 chairs + Cost of 2 tables
$
   = Rs.450 + Rs.1200 \\
   = Rs.1650 \\
$
So the value of Q comes out to be Rs.1650.
Thus, we will fill Q = Rs. 1650 in the second blank.

(iii) In this question we need to find the ratio of boys to total students in a class, given that the numbers of boys in the class are 36 while the number of girls is 18.
Now, to find the ratio of boys to the total students in the class, first we need to calculate the total number of students in the class.
So if number of boys = 36
Number of girls = 18
Then total number of students in class = number of boys + number of girls
$
   = 36 + 18 \\
   = 54 \\
$
So, the total number of students in class = 54.
Now, we have to find R which is the ratio of the number of boys to total students in class.
So,$R = \dfrac{\rm{{number \space of \space boys}}}{\rm{{total \space students \space in \space class}}}$ ,
So, putting number of boys as 36 and total number of students in class as 54 the value of R will now become:
$R = \dfrac{{36}}{{54}} = \dfrac{2}{3}$
That is, the ratio R is$2:3$ .
So, we will put $R = 2:3$ in the third blank.
Now, after solving each part, therefore the correct answer is option C.

Note: Just like direct unitary method, its converse, that is, inverse unitary method also finds its uses in various branches where the quantities and their rate of change are inversely proportional. For example, in time-work problems, the amount of work done by a labor in one day will be lesser, whereas more are the number of laborers, lesser will be time required for doing the work. Another example is in fluids, greater is the radius of the tap, lesser is the time taken to fill the utensil and vice versa.