**> Ranking and Ordering: Introduction**

**> Ranking and Ordering: Solved Examples**

**> Ranking and Ordering: Solved Examples – 2**

**> Ranking and Ordering: Solved Examples – 3**

**> Ranking and Ordering: Solved Examples – 4**

**> Ranking and Ordering: Solved Examples – 5**

**> Ranking and Ordering: Solved Examples – 6**

**> Ranking and Ordering: Solved Examples – 7**

**> Ranking and Ordering: Solved Examples – 8**

**> Ranking and Ordering: Solved Examples – 11**

**> Ranking and Ordering: Solved Examples – 12**

**> Ranking and Ordering: Solved Examples – 13**

**> Ranking and Ordering: Solved Examples – 14**

**> Ranking and Ordering: Solved Examples – 15**

**> Ranking and Ordering: Solved Examples – 16**

**> Ranking and Ordering: Solved Examples – 17**

**Practice Exercise 1: Four tests—Physics, Chemistry, Mathematics, and Biology are to be conducted on four consecutive days, not necessarily in the same order. The Physics test is held before the test which is conducted after Biology. Chemistry test is conducted exactly after two tests are held. Which is the last test held?**

A. Physics

B. Biology

C. Mathematics

D. Chemistry

**The Physics test is held before the test which is conducted after Biology. Chemistry test is conducted exactly after two tests are held.**

This implies the Chemistry test is held on the third day.

There are two possible cases:

**Case 1:** The Physics test is held on the first day, Biology test on the second day, Chemistry test on the third day, and the Mathematics test on the fourth day.

**Case 2:** The Biology test is held on the first day, Physics test on the second day, Chemistry test on the third day, and the Mathematics test on the fourth day.

In both cases, the Mathematics test is held on the last day.** So, C is the correct option.**

**Practice Exercise 2: In a test, Randhir obtained more marks than the total marks obtained by Kunal and Debu. The total marks obtained by Kunal and Shankar are more than those of Randhir. Sonal obtained more marks than Shankar. Neha obtained more marks than Randhir. Who amongst them obtained highest marks?**

A. Randhir

B. Neha

C. Sonal

D. Data is inadequate

**> Randhir obtained more marks than the total marks obtained by Kunal and Debu.**

Marks: Randhir > Kunal + Debu

**> The total marks obtained by Kunal and Shankar are more than those of Randhir. **

Marks: Kunal + Shankar > Randhir

**> Sonal obtained more marks than Shankar. Neha obtained more marks than Randhir.**

Marks: Sonal > Shankar and Neha > Randhir

Clearly, the data is inadequate to determine who got the highest marks. **So, D is the correct option.**

**Practice Exercise 3: The sum of income of A and B is more than that of C and D taken together. The sum of income of A and C is the same as that of B and D taken together. Moreover, A earns half as much as the sum of the income of B and D. Whose income is the highest?**

a. A

b. B

c. C

d. D

**> The sum of income of A and B is more than that of C and D taken together. **

Income: A + B > C + D

**> The sum of income of A and C is the same as that of B and D taken together. **

Income: A + C = B + D

This implies B’s income is more than that of C, and A’s income is more than that of D.

**> A earns half as much as the sum of the income of B and D.**

Income: A = (B + D)/2

A’s income is more than that of D. Therefore, it is less than that of B.

Hence, B’s income is the highest.** So, (b) is the correct option.**

**Practice Exercise 4: There are three pillars X, Y and Z of different heights. Three spiders A, B, and C start to climb on these pillars simultaneously. In one chance, A climbs on X by 6 cm but slips down 1 cm. B climbs on Y by 7 cm but slips down 3 cm. C climbs on Z by 6.5 cm but slips down 2 cm. If each of them requires 40 chances to reach the top of the pillars, what is the height of the shortest pillar?**

A. 161 cm

B. 163 cm

C. 182 cm

D. 210 cm

Distance by which A climb on X in 1 chance = 6 cm – 1 cm = 5 cm

Distance by which B climb on Y in 1 chance = 7 cm – 3 cm = 4 cm

Distance by which C climb on Z in 1 chance = 6.5 cm – 2 cm = 4.5 cm

Therefore, Height of pillar X = 5 cm × 39 + 6 cm = 201 cm

Height of pillar Y = 4 cm × 39 + 7 cm = 163 cm

Height of pillar Z = 4.5 cm × 39 + 6.5 cm = 182 cm

Pillar Y is the shortest and its height is 163 cm. **So, B is the correct option.**

We didn’t take into account the slip for the last chance as the spider would slip down after reaching the top.

**Practice Exercise 5: 15 students failed in a class of 52. After removing the names of failed students, a merit order list has been prepared in which the position of Ramesh is 22nd from the top. What is his position from the bottom?**

A. 18th

B. 17th

C. 16th

D. 15th

Number of students who passed the exam = 52 – 15 = 37

Therefore, Ramesh’s position from the bottom = (Number of students who passed the exam) – (Ramesh’s position from the top) + 1

= 37 – 22 + 1 = 16th

**Hence, C is the correct option.**

**Practice Exercise 6: Consider the following statements:**

**1. Either A and B are of the same age or A is older than B**

**2. Either C and D are of the same age or D is older than C**

**3. B is older than C**

**Which of the following conclusions can be drawn from the above statements?**

A. A is older than B.

B. B and D are of the same age.

C. D is older than C.

D. A is older than C.

**1. Either A and B are of the same age or A is older than B.**

Age: A = B or A > B

**2. Either C and D are of the same age or D is older than C.**

Age: C = D or D > C

**3. B is older than C.**

Age: B > C

Clearly, A must be older than C. **So, D is the correct option.**

**Practice Exercise 7: Study the information given below and answer the questions based on it.**

**A blacksmith has five iron articles A, B, C, D, and E, each having a different weight.**

**(i) A weighs twice as much as B.**

**(ii) B weights four-and-a-half times as much as C.**

**(iii) C weights half as much as D.**

**(iv) D weights half as much as E.**

**(v) E weighs less than A but more than C.**

**1. **Which of the following is lightest in weight?

A. C

B. B

C. A

D. D

**2.** E is lighter in weight than which of the other two articles?

A. A, C

B. D, C

C. A, B

D. D, B

**3. **E is heavier than which of the following two articles?

A. A, C

B. D, C

C. D, B

D. A, B

**4. **Which of the following articles is the heaviest in weight?

A. C

B. B

C. A

D. D

Suppose the weight of C is ‘x’ units. Then,

> Weight of B = 4.5x

> Weight of A = 9x

> Weight of D = 2x

> Weight of E = 4x

Therefore, Decreasing order of iron articles in terms of their weight = A > B > E > D > C

**1. **C is lightest in weight. **So, A is the correct option.**

**2. **E is lighter in weight than A and B. **So, C is the correct option.**

**3. **E is heavier than D and C. **So, B is the correct option.**

**4. **A is the heaviest in weight. **So, C is the correct option.**