JIPMAT 2022 Question Paper

Let the two-digit number be "ab". This can be represented as 10a + b

A two-digit number is 7 times the sum of its two digits.

10a + b = 7a + 7b

a = 2b

Number formed by reversing the digits = "ba" = 10b + a

The reversed number is 18 less than the original number.

10b + a = 10a + b -18

9a - 9b = 18

9(2b) - 9b = 18

b = 2

Thus, a = 2b = 4

Thus, the two-digit number is 42. 

$$b+c=\dfrac{a}{k}\rightarrow1$$

$$c+a=\dfrac{b}{k}\rightarrow2$$

$$a+b=\dfrac{c}{k}\rightarrow3$$

Adding eq. 1, eq. 2 and eq. 3

$$2(a+b+c)=\dfrac{a+b+c}{k}$$

$$k=\dfrac{1}{2}$$

Subtracing eq. 2 from eq. 1

$$a-b=\dfrac{b-a}{k}$$

$$k=-1$$

Thus, k can be either $$k=\dfrac{1}{2}$$ or $$k=-1$$

The equation of the circle is given by $$\left(x-a\right)^2+\left(y-b\right)^2=r^2$$, where $$(a,b)$$ represents the center of the circle and $$r$$ represents the radius of the circle.

We know the centre of the circle is at (2,2) 

$$\left(x-2\right)^2+\left(y-2\right)^2=r^2$$

Also, the circle is passing through the point (4,5). Thus, we can substitute x = 4 and y = 5 -

$$\left(4-2\right)^2+\left(5-2\right)^2=r^2$$

$$r^2=4+9$$

$$r^2=13$$

Thus, the equation of the circle can be given as $$\left(x-a\right)^2+\left(y-b\right)^2=13$$

Total taxed over all years = 32.0 + 34.6 + 38.8 + 42.4 + 42.6 = 190.4

Total cost of components = 296 + 332 + 382 + 410 + 428 = 1848

Ratio = $$\dfrac{190.4}{1848}=0.103$$

We have to do a hit-and-trial for each option.

(A) $$\dfrac{1}{117}=0.008$$

(B) $$\dfrac{3}{70}=0.042$$

(C) $$\dfrac{14}{138}=0.101$$

(D) $$\dfrac{12}{141}=0.085$$

The closest is Option (C)

Total Expenditure in 2000 = 288 + 296 + 26.4 + 12.2 + 32.0 = 654.6

Total Expenditure in 2003 = 305 + 410 + 28.6 + 15.2 + 42.4 = 801.2

$$\%age=\dfrac{654.6}{810.2}\times100=80.79\%$$

The closest %age is OPTION B, thus, it is the correct answer. 

%age increase in salary in 2001 = $$\dfrac{11}{288}\times100=3.82\%$$

%age increase in salary in 2002 = No increase. There was a decrease in the salary.

%age increase in salary in 2003 = $$\dfrac{7}{298}\times100=2.35\%$$

%age increase in salary in 2004 = $$\dfrac{11}{305}\times100=3.61\%$$

Highest %age increase is in 2001. 

50% of the students are girls. Thus, the total number of students must be 80. 

Half the students have grades A and B. This means that 40 students have grades A and B. Now, 30 students have grade B, thus 10 students will have grade A.

Thus, 40 students will have grade C.

5 boys have grade A, and in total 10 students have grade A. Thus, 5 girls will have grade A. 

25% of the boys have grade C; thus, 25% of 40 = 10 boys have grade C.

Now, 5 boys have grade A and 10 boys have grade C, and there are a total of 40 students, thus 25 boys will get grade B. 

10 boys have grade C, and a total of 40 students got grade C. Thus, 30 girls will get grade C.

25 boys have grade B, and a total of 30 students got grade B. Thus, 5 girls will get grade B. 

The number of girls who have grade B and grade C are 5 and 30, respectively. 

50% of the students are girls. Thus, the total number of students must be 80. 

Half the students have grades A and B. This means that 40 students have grades A and B. Now, 30 students have grade B, thus 10 students will have grade A.

Thus, 40 students will have grade C.

5 boys have grade A, and in total 10 students have grade A. Thus, 5 girls will have grade A. 

25% of the boys have grade C; thus, 25% of 40 = 10 boys have grade C.

Now, 5 boys have grade A and 10 boys have grade C, and there are a total of 40 students, thus 25 boys will get grade B. 

10 boys have grade C, and a total of 40 students got grade C. Thus, 30 girls will get grade C.

25 boys have grade B, and a total of 30 students got grade B. Thus, 5 girls will get grade B. 

Total number of girls = 40

Total number of boys = 40

Total students = 80

50% of the students are girls. Thus, the total number of students must be 80. 

Half the students have grades A and B. This means that 40 students have grades A and B. Now, 30 students have grade B, thus 10 students will have grade A.

Thus, 40 students will have grade C.

5 boys have grade A, and in total 10 students have grade A. Thus, 5 girls will have grade A. 

25% of the boys have grade C; thus, 25% of 40 = 10 boys have grade C.

Now, 5 boys have grade A and 10 boys have grade C, and there are a total of 40 students, thus 25 boys will get grade B. 

10 boys have grade C, and a total of 40 students got grade C. Thus, 30 girls will get grade C.

25 boys have grade B, and a total of 30 students got grade B. Thus, 5 girls will get grade B. 

Number of girls having grade 'A' = 5 

Total students having grade 'A' = 10.

50% of the students are girls. Thus, the total number of students must be 80. 

Half the students have grades A and B. This means that 40 students have grades A and B. Now, 30 students have grade B, thus 10 students will have grade A.

Thus, 40 students will have grade C.

5 boys have grade A, and in total 10 students have grade A. Thus, 5 girls will have grade A. 

25% of the boys have grade C; thus, 25% of 40 = 10 boys have grade C.

Now, 5 boys have grade A and 10 boys have grade C, and there are a total of 40 students, thus 25 boys will get grade B. 

10 boys have grade C, and a total of 40 students got grade C. Thus, 30 girls will get grade C.

25 boys have grade B, and a total of 30 students got grade B. Thus, 5 girls will get grade B. 

The number of boys who have grades B and C are 25 and 10, respectively.