LOGICAL REASONING- INTRODUCTION

WHAT IS LOGICAL REASONING? Logic plays a very important role in our day to day life in ascertaining what is more credible or which reasoning is sounder. When we face a problem or situation, we tend to apply logic to arrive at the most desired decision. Logic can be seen as a tool using which we find out the strength of reasoning. Logical Reasoning consists of question types which test both your mathematical and logical abilities. Logical Reasoning, though based on common sense ,it goes a little beyond. Hence, it needs a higher level of thinking –more critical and more analytical, before we act upon something. These questions are there in most of the examinations, and present an interesting challenge to students. While some of these questions can appear difficult and time consuming, many are not too difficult if one has practiced in a regular manner. In reasoning based questions, one is required to break down the given information in smaller components and organise the information provided in a systematic fashion. One must first get a sense of the overall shape of the program and then see how individual pieces of information fit into it.

TIPS AND GUIDELINES

Before you try to answer a few sample questions, here are some general test-taking tips that should help you with the Logical Reasoning section :

• Do not assume any information • Read everything carefully. Read the lines below any given figure carefully • Make a wise caselet/question selection-Work out the strategy • Write down all the given information • Pay special attention to words like "all," "some," or "none" when you read the factual information each question

gives you. Other qualifying words such as "other than," "only" or "unless" are important, too. • Pay attention to negative prefixes also, such as non-, un-, or dis-. • A valid conclusion is the one that definitely follows from the information you are given. An invalid conclusion is the

one that definitely does not follow from the information. • Be sure to read all the response choices carefully before choosing one.

TYPES OF QUESTIONS

Blood Relations

Arrangements

Tournaments

Rankings

Sequence & Series

Condition Based

Miscellaneous

Deductive Logic

TYPES

BLOOD RELATIONS

Family relation / Family tree / Bloodline related aptitude questions are pretty common in IIFT, SNAP, CMAT , CET and TISS . Questions on Blood Relationship are related to our day to day life. We are bound by our kith and kin through a chain of relationships. Normally the questions on blood relations express a lengthy complicated relation for a short, simple and direct relation. So in order to solve these type questions, one should be thorough with blood relations and also be in a position to relate the people by analysing the given statements . EXAMPLE 1: ‘B’ is the father of ‘C’ but ‘C’ is not his son. ‘Q’ is the daughter of ‘C’.’A’ is the spouse of ‘B’. ‘P’ is the brother of ‘C’. ‘R’ is the son of ‘P’. ‘S’ is the spouse of ‘P’. ‘T’ is the father of ‘S’. Who is the grand daughter of ‘B’? (A) R (B) P (C) Q (D) C (E) None of these SOLUTION : C

EXPLANATION : ‘B’ is the father of ‘C’ but ‘C’ is not his son. ‘C’ is thus the daughter of ‘B’. ‘Q’ is the daughter of ‘C’. So, ‘Q’ is the granddaughter of B’. Hence, answer is (C) Q. B Sp A T D f C B P(g) Sp S(fe) D sn Q R EXAMPLE 2 : ‘S’ and ‘L’ are two sons of ‘M’. ‘Q’ is the mother of ‘P’ who is the only sister of ‘L’. ‘G’ is the wife of ‘R’ who is the son of ‘K’. ‘M’ is the brother of ‘G’. Which of the following statements is not true? A. S is the brother of P B. G is the aunt of S C. R is the brother-in-law of M D. G is the daughter of K E. None of these

SOLUTION : D EXPLANATION : ‘S’ and ‘L’ are the two sons of ‘M’ and ‘Q’ is the mother of ‘P’ who is the only sister of ‘L’. So ‘P’ is also sister of ‘S’ who is the brother of ‘L’. So the first statement is true. As ‘M’ is the brother of ‘G’ and ‘G’ is the wife of ‘R’, so ‘G’ will be aunt of ‘S’, ‘L’ and ‘P’. So the second statement ‘G’ is the aunt of ‘S’ is also true.As ‘M’ is the brother of ‘G’ and ‘G’ is the wife of ‘R’. So the third statement that ‘R’ is the brother-inlaw of ‘M’ is true. ‘G’ is the wife of ‘R’ who is the son of ‘K’. So ‘G’ is the daughter-in-law of ‘K’. Hence the fourth statement that ‘G’ is the daughter of ‘K’ is not true. The answer is (D) G is the daughter of K. K sn R(g) w G(fe) b M(h) Q(w) sn sn m S L P b s

EXAMPLE 3: In a joint family, there are father, mother, 3 married daughters and one unmarried son. Of the daughters, two have 2 sons each, and one has a daughter. How many male members are there in the family? (A) 3 (B) 2 (C) 6 (D) 9 (E) None of these

SOLUTION : D EXPLANATION : The male members in the family are father, husbands of 3 married daughters, unmarried son and 2 sons of each of two daughters. So number of male members = (1+ 3 + 1 + 2 x 2) = 9. Hence, answer is (D) 9. EXAMPLE 4: Read the following information carefully and answer the questions given below: I. ‘P # Q’ means ‘P is the father of Q’. II. ‘P + Q’ means ‘P is the mother of Q’ III. ‘P – Q’ means ‘P is the brother of Q’. IV. ‘P % Q’ means ‘P is the sister of Q’ If A + B – C % D # E, then A is D’s (A) Father (B) Sister (C) Grandfather (D) Grandmother (E) None of these

SOLUTION : D EXPLANATION : A + B # C – D means A is the mother of B, who is the father of C, who is the brother of D. This can be better understood by way of a diagram as follow A m ?(gm) B f f C D b EXAMPLE 5 : Kanchan is mother-in-law of Rita who is sister-in-law of Vinay. Dashahrat is father of Sham, the only brother of Vinay. How is Kanchan related to Sham? (A) Mother (B) Wife (C) Mother-in-law (D) Aunt (E) None of these SOLUTION :A EXPLANATION :Rita is sister-in-law of Vinay means Vinay is the brother of Rita’s husband. But Vinay has only one brother, Sham. So, Sham is Rita’s husband. Kanchan is mother-in-law of Rita means Kanchan is the mother of Rita’s husband i.e. Sham. So Kanchan is the mother of Sham. Hence, the answer is (A) Mother.

ARRANGEMENTS

The process of making a group of people to sit as per a prefixed manner is called SEATING ARRANGEMENT. In these questions some conditions are given, on the basis of which students are required to arrange objects, either in a row or in circular order. While making arrangements , it should be noted that all conditions given are compiled with. These type of questions generally involve five to eight individuals arranged in a certain manner. They may have to be arranged in a row or a circle Sometimes these questions are made more difficult by allowing an individual to a particular position with some conditions. There are multiple types of questions which are asked from the topic ‘Seating Arrangement’, so it is quite difficult to predict exact type of questions that are asked, but on the basis of Observation, Analysis and Experience, here we are giving different types of questions that are usually asked in the examination. Type 1- Linear arrangement Type 2-Circular arrangement

TYPE 1- LINEAR ARRANGEMENT : In this type of arrangement, we arrange people or objects in a line or row .The arrangement is done only on one ‘axis’ and hence, the position of people or objects assumes importance in terms of order like first position, second position....last position. In this type of arrangement , we take according to our left and right. There are few words which must be paid adequate attention i.e. ‘between’ means ‘sandwiched , ‘immediate left’ is different from ‘ to the left’ . Further this can be divided into two types : •One Row Sequence •Two Row Sequence

One Row Sequence Five of India’s leading models are posing for a photograph promoting “world peace and understanding”. But then, Rakesh Shreshtha the photographer is having a tough time getting them to stand in a straight line, because Aishwarya refuses to stand next to Sushmita because Sushmita had said something about her in a leading gossip magazine. Rachel and Anu want to stand together because they are “such good friends”. Manpreet, on the other hand cannot get along well with Rachel, because there is some talk about Rachel scheming to get a contract already awarded to Manpreet. Anu believes her friendly astrologer who has asked her to stand at the extreme right for all group photographs. Finally, Rakesh managed to pacify the girls and got a beautiful picture of five beautiful girls smiling beautifully in a beautiful straight line, promoting world peace. Question 1: If Aishwarya is standing to the extreme left, which is the girl standing in the middle? (A) Manpreet (B) Sushmita (C) Rachel (D) Cannot say Question 2: If Aishwarya stands to the extreme left, which is the girl who stands second from left? (A) Cannot say (B) Sushmita (C) Rachel (D) Manpreet Question 3 : If Anu’s astrologer tells her to stand second from left and Aishwarya decides to stand second from right, then who is the girl standing on the extreme right? (A) Rachel (B) Sushmita (C) Cannot say (D) Manpreet

SOLUTION : B, D, D EXPLANATION :

From the given conditions the only arrangements that are possible is: LEFT RIGHT Sushmita Manpreet Aishwarya Rachel Anu OR Aishwarya Manpreet Sushmita Rachel Anu Answer 1: If Aishwarya is standing at the extreme left, the latter arrangement holds good. Hence it is Sushmita who isvstanding in the middle. Answer 2: Again the latter arrangement holds good. So the girl who is standing second from left is Manpreet. Answer 3: For the given conditions, the following arrangement is possible: (LEFT) Sushmita Anu Rachel Aishwarya Manpreet (RIGHT) Hence, Manpreet is standing on the extreme right.

Two Row Sequence An Indo-China joint venture by the name of Chindia Corp Ltd has eight board members – L, M, N, P, Q, R,S and T – four each from India and China. The four members from each country hold different posts among COO, CFO, CMD and CEO, in no particular order. During a board meeting, the eight members sit at a square table such that there are two members along each side of the table. It is also known that: I. No member has any of his fellow countrymen as neighbours. II. No two members sitting along the same side of the table hold the same post in their respective countries. III. L, who is a CFO, and P sit along the same side of the table. IV. The two neighbours of N are the Indian CFO and S. V. R is a COO and exactly one person sits between him and the Chinese CMD. VI. Q, who is a CFO, is the third person to the right of L. VII. M, who is a COO, sits diagonally opposite S. A CMD sits to the immediate right of S. Question 1: Who is the Chinese CEO? (a) P (b) T (c) N (d) Cannot be determined

Question 2: Which two members among the given pairs cannot be neighbours? (a) P and M (b) M and N (c) M and T (d) M and Q

Question 3: If the two COOs are neighbours, which of the following is the correct combination of “name – post” of the third person to the left of T? (a) P – CEO (b) L – CFO (c) Q – CFO (d) R – COO

SOLUTION : D, B, C EXPLANATION : 6 5 7 4 8 3 1 2 From statement (i), we can deduce that the Indian and the Chinese members are seated alternately. Also, from statements (iv), (v) and (vii), M and S are Indian and N and R are Chinese. Let us first fix the positions of P and L. Suppose P is to the right of L. Two cases arise – L is either a Chinese or an Indian. Case I: L is a Chinese and seated at position 1, therefore, positions 1, 3, 5 and 7 are occupied by Chinese and the rest by Indians. Then Q, the Indian CFO, must be seated at position 4. M and S, both Indians, sit at diagonally opposite positions as per statement (vii), which is not possible. Case II: L is an Indian and seated at position 1, therefore, positions 1, 3, 5 and 7 are occupied by Indians and the rest by Chinese. Then Q, the Chinese CFO, must be seated at position 4. From statements (iv) and (v), N, a CMD, must be sitting at position 8. Therefore, M, R and S sit at positions 3, 6 and 7 respectively. Further analysis gives the following arrangement :

Similarly, we will arrive at the following arrangement if P is to the left of L.

T

Q

M

S

N

P L

R

Q

N

S

M

T

L P

R

TYPE 2- CIRCULAR ARRANGEMENT In this type of arrangement we arrange people or objects around a circle or a table. CIRCULAR SEQUENCE : In this arrangement, some person are sitting around a circle and they are facing the centre. RIGHT LEFT LEFT RIGHT RIGHT LEFT LEFT RIGHT Left movement is called clockwise rotation and Right movement is called anti-clockwise rotation. The information given in questions specify the position of some or all the person in the arrangement. The position are specified through various conditions. In order to solve such questions, first of all diagram should be made. By doing so questions are easily and quickly solved.

EXAMAPLE 1: P, Q, R, S, T, U, V and W are sitting round the circle and are facing the centre: P is second to the right of T who is the neighbour of R and V. S is not the neighbour of P. V is the neighbour of U. Q is not between S and W. W is not between U and S. Which two of the following are not neighbours ? A. RV B. UV C.RP D. QW

SOLUTION : A Q W P S R U T V

EXAMPLE 2 : Eight people S, R, N, L, M, T, O and P are sitting in a circle facing the centre. All eight belong to different professions - reporter, doctor, cricketer, teacher, accountant, shopkeeper, painter and supervisor. They are not necessarily seated in the mentioned order. M is sitting third to the left of O. The doctor is to the immediate right of M and M is not a reporter. R is sitting fourth to the right of P. Neither R nor P is an immediate neighbour of M. T is a teacher and is sitting third to the right of the doctor. The shopkeeper is sitting second to the left of the teacher. The painter is sitting second to the left of M. S is the cricketer is sitting exactly between T and P. The accountant is sitting second to the right of the cricketer. N is sitting third to the left of T. QUESTION 1. Who amongst the following is a reporter? (A) O (B) L (C) N (D) R (E) None of these QUESTION 2. What is S’s position with respect to R? (A) Third to the right (B) Second to the right (C) Third to the left (D) Second to the left (E) Fourth to the right SOLUTION : A, B

EXPLANATION : M L N R P O S T

M Supervisor

L Accountant

P Painter

S Cricketer

T Teacher

O Reporter

R Shopkeeper

N Doctor

TOURNAMENT BASED

In Logical Reasoning, very often we encounter problems based on games or tournaments. Such tournament based format offers the examiner a multitude of options. So, there cannot be a set formula for solving such kind of questions. Let us understand these with couple of examples . EXAMPLE 1 : Seven chess players participated in a chess tournament. The players were ranked from 1 to 7,based on their ratings before the tournament. In the tournament, each player played two games against every other player i.e. one game with black pieces and the other with white pieces .The games were scheduled on consecutive days such that on any day exactly three games were scheduled involving six of the seven players ,while the remaining player was rested on that day and no particular order was followed for resting the players. For any player one point was awarded for a win, half a point for a draw and zero points for a loss. The person with the highest total number of total points at the end of the tournament is said to have finished first, the one with the next highest total points, second and so on. If two or more players end up with the same total number of total points their ranks before the tournament are considered and the one with the best rank (numerically lowest) before the tournament is considered to have finished ahead of the other players.

Question 1 : Which of the following cannot be the total number of points of the player who finished first? (a) 6 (b) 7 (c) 8 (d) None of These Question 2: If exactly one player ended up with the highest total number of points ,what is the minm possible difference between the points of the player who finished first and that of the player who finished last in the tournament?

(a) 0.5 (b)1 (c) 1.5 (d)2.0

Question 3 :If the winner had 9.5 points ,which of the following can be the number of points scored by the player who finished last?

(a) 4.5 (b)6.5 (c) 5.5 (d) None Of these

Question 4 :At the end of the tournament it was found that only players A and B finished with the same number of points and no other pair of players from the seven players finished with the same points .what is the minimum possible total number of points of the person who finished first?

(a) 6.5 (b) 7 (c) 7.5 (d)8

SOLUTION : D, B,A EXPLANATION : 1) Total number of points are 7c2*2 =42 thus if each person gets equal points and then according to their previous rank they can be adjudged first thus the minimum points required for getting first are 6 and all marks more then 6 will certainly result in a winner. 2) Since only one player ended up with the highest total number of points and we have to find the minimum possible difference between the points of the player who finished first and that of the player who finished last in the tournament. So 1st rank should get minimum marks and all other get equal marks thus first one gets 6.5 and remaining 5 gets 6 and last one 5.5. 3) 42-9.5=32.5 32.5/6=5.4 Thus last one cannot get more than 5.4 marks Thus he gets 4.5 marks (only option left)

4)The total points = Total number of matches (as 1 point would be given out per match whatever the result) = 7C2*2 = 42 If the first person gets 6.5 Then max sum can be 6.5+6.5+6+5.5+5+4.5+4=38 Thus it cannot be the answer If first person gets 7 7+7+6.5+6+5.5+5+4.5=41.5 Thus it cannot be the answer If first person gets 7.5 Then 7.5+7.5+7+6.5+6+5.5+2 = 42 There can be more than one situation For eg. 7.5+7+7+6.5+6+5.5+2.5 = 42 So, 7.5 is the answer

RANKINGS

EXAMPLE 1: During a cycle racing event in 2008 Olympic Games, eight riders – Alex, Fausto, Hilton, Jason, Matt, Nathan, Rahsaan and Ryan – cycled in eight different lanes on a track. The lanes were numbered 1 to 8 from left to right in that order. In a strange coincidence, the finishing positions of all the riders were same as their lane numbers. E.g. the rider cycling in the lane numbered 1 finished first, the rider cycling in the lane numbered 2 finished second and so on. It is also known that: (i) Exactly two riders finished between Hilton and Rahsaan. (ii) Jason finished just ahead of Rahsaan. (iii) Nathan finished just ahead of Alex. (iv) Jason finished ahead of Hilton. (v) Neither Matt nor Ryan finished last. (vi) Exactly two riders finished ahead of Jason. 1. Who could not have finished fifth in the race? (a) Alex (b) Matt (c) Nathan (d) Ryan

2. Who finished seventh and eighth respectively in the race? (a) Rahsaan and Fausto (b) Hilton and Fausto (c) Jason and Hilton (d) Cannot be determined

SOLUTION : A,B EXPLANATION : 1. From statements (ii) and (vi), Jason and Rahsaan were cycling in the lanes numbered 3 and 4 respectively. From statements (i) and (iv), Hilton was in the lane numbered 7. From statements (iii) and (v), either Alex or Fausto was in the lane numbered 8. But since Hilton was in the lane numbered 7, Alex could not have been in the lane numbered 8. Therefore, Fausto was in the lane numbered 8. Now two cases are possible: Case I: Nathan and Alex were in the lanes numbered 1 and 2 respectively. Matt and Ryan were in the lanes numbered 5 and 6, in no particular order Case II: Nathan and Alex were in the lanes numbered 5 and 6 respectively. Matt and Ryan were in the lanes numbered 1 and 2, in no particular order.

LANE 1 2 3 4 5 6 7 8

RIDER Nathan

Alex Jason Rahsaan Matt/ Ryan

Ryan/ Matt

Hilton Fausto

EXAMPLE 2 : Niret, Priya, Rehan, Soni and Usha appeared in two tests, one each of Physics and Chemistry. They were ranked 1 to 5 in each test based on their performances. None of them secured the same rank in the two subjects. In the Physics test, Rehan’s rank was better than that of Soni while Niret’s rank was the worst among the five. Usha was the only one who was among the bottom two in both the tests. Priya secured Rank 3 in the Chemistry test. The number of students who got ranks between Niret and Rehan was equal in the two tests. What was the rank of Rehan in the Chemistry test? (a) 2 (b) 1 (c) 4 (d) Cannot be determined SOLUTION : C

LANE 1 2 3 4 5 6 7 8

RIDER Matt/ Ryan

Matt/ Ryan

Jason Rahsaan Nathan Alex

Hilton Fausto

EXPLANATION : As Niret got Rank 5 in Physics, Usha must have got Rank 4 and Rank 5 in Physics and Chemistry respectively. Since Rehan’s rank was better than Soni’s rank in Physics, Rehan must have secured either Rank 1 or Rank 2. However, had Rehan got Rank 1 in Physics, the number of students with ranks between Niret and Rehan could not have been equal in the two tests. So, Rehan must have secured Rank 2 in Physics. Since there were two people between Niret and Rehan in Physics, they must have got Ranks 1 and 4 in Chemistry. Niret could not have got Rank 4 as he, in that case, would have become the second person besides Usha to be in the bottom two in both the tests. The final arrangement is given below : As we can see, Rehan got Rank 4 in Chemistry

1 2 3 4 5

PHYSICS Priya Rehan Soni Usha Niret

CHEMISTRY Niret Soni Priya Rehan Usha

MISCELLANOUS

EXAMPLE 1 : Each of the four diplomats – Kabir, Laxman, Manan and Nayodita – worked for an integral number of years in each of the three countries – the USA, the UK and China. The sums of the number of years spent in the three countries together were distinct for the four diplomats. The sums of the number of years spent by the four diplomats together in the USA, the UK and China were 11, 13 and 13 respectively. No diplomat spent an equal number of years in any two countries. No two diplomats spent an equal number of years in any country. It is also known that: I. The number of years spent by Kabir and Manan in China were 4 and 1 respectively. II. The sum of the number of years spent in the three countries together by Manan was not less than III. that of Kabir. IV. The sum of the number of years spent in the three countries together by Laxman was 15. V. The absolute difference between the number of years spent by Kabir in the USA and the number of years spent by

Manan in the UK was 2. VI. Among the three countries, Nayodita spent the least time in the UK and the maximum in China.

1. What was the number of year(s) spent by Nayodita in the UK? (a) 2 (b) 1 (c) 4 (d) 3 2. What was the difference between the number of years spent by Manan in the USA and Nayodita in China? (a) 2 (b) 1 (c) 0 (d) 3 3. Among the four diplomats, who spent the least time in China? (a) Manan (b) Laxman (c) Kabir (d) Nayodita SOLUTION : B, A , A EXPLANATION : As no diplomat spent an equal number of years in any two countries, each diplomat must have spent at least 6 years (1 + 2 + 3) in the three countries together. The total number of years spent by the four diplomats in the three countries = 11 + 13 + 13 = 37. From statement (iii), Laxman spent 15 years in the three countries together, therefore, the total number of years spent by the other three diplomats was 37 – 15 = 22.

From statement (i), Kabir must have spent at least 7 years in the three countries together as he had spent 4 years in China alone. From statement (ii), the total number of years spent by Manan in the three countries together was not less than that of Kabir. The only possibility is that Kabir spent 7 years, and Manan and Nayodita spent 9 years and 6 years respectively. Using statements (v), (iv) and (i) in that order along with the conclusions drawn above, the final distribution can be tabulated as given below.

USA UK CHINA TOTAL

KABIR 1 2 4 7

LAXMAN 3 7 5 15

MANAN 5 3 1 9

NAYODITA 2 1 3 6

TOTAL 11 13 13 37

EXAMPLE 2 : Each of the six men – Akrosh, Arun, Lakshya, Manav, Shandu and Sujeet – got married to a different woman among Aditi, Ishita, Nisha, Rozy, Shilpi and Sona in the year 2012. The marriages happened on six different dates – 27th January, 10th February, 17th April, 26th April, 12th May and 8th June – and at six different places – Agra, Auli, Corbett, Dalhousie, Mussoorie and Shimla, in no particular order. It is also known that: (i) The marriage of Nisha and Arun took place on 10th February and that of Aditi on 17th April. (ii) Shilpi’s marriage took place in Mussoorie. It happened after Lakshya’s marriage and did not happen on 8th June. Page 16 Proctored Mock CAT-5 2012 (iii) Ishita’s marriage took place in Auli and she did not get married to Lakshya. She got married before Akrosh but not in January. (iv) Sona and Shandu got married in Corbett. The marriage did not happen in January. (v) Rozy got married to either Manav or Akrosh. (vi) Neither Nisha’s nor Aditi’s marriage took place in Dalhousie.

1. Who got married to Shilpi? (a) Akrosh (b) Manav (c) Sujeet (d) Cannot be determined 2. Which of the following is a correct combination of person and his date of marriage? (a) Lakshya – 27th January (b) Akrosh – 8th June (c) Sujeet – 26th April (d) None of these 3. Where did the marriage that happened on 8th June take place? (a) Mussoorie (b) Agra (c) Corbett (d) Either (a) or (c)

SOLUTION : A, C, C EXPLANATION : Since Lakshya did not get married to Nisha, Shilpi, Ishita, Sona or Rozy, he must have got married to Aditi on 17th April. As none of Nisha, Shilpi, Ishita, Sona and Aditi got married on 27th January, Rozy must have got married on 27th January. From statements (iii) and (iv), we can conclude that Rozy got married to Manav.

Since none of Nisha, Ishita, Sona, Rozy and Aditi got married to Akrosh, Shilpi must have got married to Akrosh. As Nisha got married to Arun and Sona got married to Shandu, Ishita must have got married to Sujeet. Since none of Nisha, Shilpi, Ishita, Rozy and Aditi got married on 8th June, Sona must have got married to Shandu on 8th June in Corbett. From statement (iii), Ishita got married before Akrosh. Hence, Akrosh must have got married to Shilpi on 12th May and Ishita to Sujeet on 26th April. Further analysis leads to the following table-

WOMAN MAN DATE PLACE

ADITI LAKSHYA 17 TH APRIL SHIMLA/AGRA

ISHITA SUJEET 26 TH APRIL AULI

NISHA ARUN 10TH FEB AGRA/SHIMLA

ROZY MANAV 27TH JANUARY DALHOUSIE

SHILPI AKROSH 12TH JUNE MUSSOORIE

SONA SHANDU 8TH JUNE CORBETT