Blood Relation

1.	Pointing to a photograph of a boy Suresh said, "He is the son of the only son of my mother." How is Suresh related to that boy?
	A. Brother B. Uncle C. Cousin D. Father Answer & Explanation Answer: Option D Explanation: The boy in the photograph is the only son of the son of Suresh's mother i.e., the son of Suresh. Hence, Suresh is the father of boy.

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2.	If A + B means A is the mother of B; A - B means A is the brother B; A % B means A is the father of B and A x B means A is the sister of B, which of the following shows that P is the maternal uncle of Q?
	A. Q - N + M x P B. P + S x N - Q C. P - M + N x Q D. Q - S % P Answer & Explanation Answer: Option C Explanation: P - M → P is the brother of M M + N → M is the mother of N N x Q → N is the sister of Q Therefore, P is the maternal uncle of Q.

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3.

If A is the brother of B; B is the sister of C; and C is the father of D, how D is related to A?

A. Brother B. Sister C. Nephew D. Cannot be determined Answer & Explanation Answer: Option D Explanation: If D is Male, the answer is Nephew. If D is Female, the answer is Niece. As the sex of D is not known, hence, the relation between D and A cannot be determined. Note: Niece - A daughter of one's brother or sister, or of one's brother-in-law or sister-in-law. Nephew - A son of one's brother or sister, or of one's brother-in-law or sister-in-law.

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4.	If A + B means A is the brother of B; A - B means A is the sister of B and A x B means A is the father of B. Which of the following means that C is the son of M?
	A. M - N x C + F B. F - C + N x M C. N + M - F x C D. M x N - C + F Answer & Explanation Answer: Option D Explanation: M x N → M is the father of N N - C → N is the sister of C and C + F → C is the brother of F. Hence, M is the father of C or C is the son of M.

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5.	Introducing a boy, a girl said, "He is the son of the daughter of the father of my uncle." How is the boy related to the girl?
	A. Brother B. Nephew C. Uncle D. Son-in-law Answer & Explanation Answer: Option A Explanation: The father of the boy's uncle → the grandfather of the boy and daughter of the grandfather → sister of father.

Reasoning Circular Sitting Arrangement

There are 4 types of ‘Logical-Arrangement’ questions

1. Circular : Sitting In a Round Table
2. Linear : Sitting in rectangular table or row
3. Traits: List of people given, A lives in Hyderabad and prefers T  and owns Maruti etc.
4. Family trees: A is the father of B who is mother Office…

These problems are quite easy to solve but can be very time-consuming if you donot proceed in a proper manner.

Circular arrangement

It is the easiest of all arrangement questions.
However one point must be kept in mind: “A is sitting adjacent to B”= Either A is on left side of B OR A is on right side of B. In short, you’ve to consider multiple possible cases during the calculation.
Let’s try a question

6 people A to F are sitting in a round table. A is not adjacent to B or C; D is not adjacent to C or E; B and C are adjacent; F is in the middle of D and C.

Step 1: Draw the diagrams

It is compulsory to draw diagram. You can’t solve the ‘circular-arrangement’ with drawing diagrams.
Ok, Lot of people are not sitting adjacent to eachother but we can’t use those “negatives” as starting-point to draw a diagram.
Better take the positive statement “B and C are adjacent” as our starting point and proceed.
There are two possible cases

• Either C is on the right side of B Or
• C is on the left side of B.

Now use another positive statement: “F is in the middle of D and C.” Fill this in given cases
New diagrams look like this

Now deal with the negative statements:”A is not adjacent to B or C”
Consider case#1: There are only two seats left: skyblue and orange colored.
But A cannot be seated in skyblue chair, because question statement says “A is not adjacent to B or C”
Therefore A can be seated only in orange chair for case #1 and
Similarly for case #2, A can be seated only in Red chair.
After A is seated, there is only one seat left and only one man (E) is left so we place him in the remaining seat.

Alright all seats are now occupied, which means we’ve to run the checklist. IT serves two purposes

• Incase you made any mistake in arrangement, you’ll find out at this stage OR
• In One of the two cases, all checklist will not ‘pass’ thus we can eliminate one possible case and will be left with final perfect correct arrangement.

Step 2: Run the Checklist

Checklist	Case 1	Case 2
A is not adjacent to B or C	Pass	Pass
D is not adjacent to C or E	Pass	Pass
B and C are adjacent	Pass	Pass
F is in the middle of D and C.	Pass	Pass

Damn it, both cases are passing the checklist. Time for some questions

Step 3: Proceed with questions

Q1. If one neighbor of A is D, who is the other one?

Both cases are valid and in both cases A is sitting between D and E.
Therefore if one neighbor of A is D, then other is E. We get same neighbor “E” in both cases.

Ans. E is the other neighbor.

Q2. Who is sitting on the left hand side of A?

Both case are valid and in first case, D is sitting on the left hand side of A.
But second case, E is sitting on the left hand side of A.
So we are not getting ‘one’ definite answer. It can be either D or E. So final answer is
Ans. No conclusion. Cannot be determined. Data insufficient. D or E.

Time and Distance

Formulae
(i) Speed = Distance/Time
(ii) x km/hr = (x × 5/18 ) m/sec.
(ii) x metres / sec = (x × 18/5 )km/hr.

1.    A man covers a certain distance between his house and office on scooter.Having an average speed of 30 km/hr, he late by 10 min. However, with a speed of 40 km/hr. he reaches his office 5 min earlier. Find the distance between his house and office.
(1) 20 km                          (2) 40 km
(3) 30 km                          (4) 25 km

2.    A man car does a journey in 10 hrs, the first half at 21 km/hr and the second half at 24 km/hr. Find the distance.
(1) 220 km                                    (2) 215 km
(3) 210 km                                    (4) 224 km

3.    Walking 3/4 of his usual speed, a person is 10 min late to his office. Find his usual time to cover the distance.
(1) 10 minutes                   (2) 50 minutes
(3) 30 minutes                   (4) None of these

4.    Running 4/3 of his usual speed, a person improves his timing by 10 minutes. Find his usual time to cover the distance.
(1) 60 minutes                   (2) 40 minutes
(3) 25 minutes                   (4) 30 minutes

5.    A train travelling 25 km an hour leaves Delhi at 9 a.m. and another train travelling 35 km an hour starts at 2 p.m. in the same direction. How many km from Delhi will they be together?
(1) 437 ½ km                    (1) 436 ½ km
(3) 435 ½ km                    (4) 434 ½ km

6.    Two men A and B walk from P to Q, a distance of 21 km, at 3 and 4 km an hour respectively. B reaches Q, returns immediately and meets A at R. Find the distance from P to R.
(1) 18 km                          (2) 20 km
(3) 35 km                          (4) 15 km

7.    A man sets out to cycle from Delhi to Rohtak, and at the same time another man starts from Rohtak to cycle to Delhi. After passing each other they complete their journeys in 3 1/3and 4 4/5hours respectively. At what rates does the second man cycle if the first cycles at 8 km per hour?
(1) 6 2/3                             (2) 5 2/3
(3) 4 2/3                             (4) None of these

8.    A monkey tries to ascend a greased pole 14 metres high. He ascends 2 metres in first minute and slipsdown 1 metre in the alternate minute. If he continues to ascend in this fashion, how long does he take to reach the top?
(1) 25 minutes                   (2) 20 minutes
(3) 15 minutes                   (4) None of these

9.    A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. Another man leaves the point Q at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
(1) 10 a.m.                         (2) 9 a.m.
(3) 9: 30 a.m.                    (4) 8 a.m

10.  Without any stoppage a person travels a certain distance at an average speed of 80 kmph, and with stoppages he covers the same distance at an average of 60 kmph. How many minutes per hour does he stop?
(1) 25minutes                    (2) 15 minutes
(3) 10 minutes                   (4) None of these


Answers  with Solution:
1.    (3) :
Solution: Let the distance be x km.
Time taken to cover x km at 30 km/hr = x/30 hrs
Time taken to cover x km at 40 km/hr = x/ 40 hrs.
Difference between the time taken = 15 min = ¼ hr.
x/30 – x/40 = ¼  or 4x – 3x = 30 or x = 30 km.

Shortcut: (Try this your self)
Required distance
= Product of two speeds/ Difference of two speeds    x Difference between arrival times.

2.    (4)
Solution:
Let the distance be x km.Then x/2 km is travelled at a speed of 21 km/hr and x/2 km at a speed of 24 km/hr.
Then time taken to travel the whole journey
= x/(2×21) + x/(2 x 24) = 10 hrs.
so, x =  224 km
Short cut : (Try this your self)
Distance =(2 x Time x S1 x S2 ) / (S1 + S2 )
Where , S1 = Speed during first half and
S2 = Speed during second half of journey

3.    (3) :
Solution:
Let the usual time be x min.
Time taken at ¾ of the usual speed = 4x/3 min
4x/3 – x = 10
x/3 = 10  à x = 30 min.
Shortcut : (Try this your self)
Usual time = Late time / ( 1 ÷ ¾  - 1)  = 10/1/3 = 30 minutes

4.    (2) Shortcut:
Improved time / (1 -  1 + 4/3 ) = 40 minutes

5.    (1) :
Solution:
The first train has a start of 25 / 5 km and the second train gains ( 35 – 25 ) or 10 km per hour.
The second train will gain 25 x 5 km in  (25 x5) / 10 or 12 ½ hours.
The required distance from Delhi = 12 ½ x 35 km = 437 ½ km

Shortcut : (try this )
Meeting point’s distance from starting point
= (S1 x S2 x Difference in time) / Difference in speed      ( S1 and S2 are the speed  )

6.    (1)
Solution:
When B meets A at R, B has walked the distance PQ + QR and A the distance PR. That is , both of them have together walked twice the distance from P to Q, i.e 42 km.
Now the rates of A and B are 3 : 4 and they have walked 42 km.
Hence the distance PR travelled by A = 3/7 of 42 km = 18 km

7.    (1)
Solution:
If two persons ( or train) A and B start at the same time in opposite directions from two points  and arrive at the pint a and b hrs respectively after having met, then
A’s rate : B’s rate = √b : √a
= (√ 4 4/5 ) / ( √3 1/3 ) = 6/5
2^nd man’s rate = 5/6 x 8  =  6 2/3 km/hr.

8.    (1)
Solution:
In every 2 minutes he is able to ascend 2 – 1 = 1 metre. This way he ascends upto 12 metres because when he reaches at the top. He does not slip down. thus, upto 12 metres he takes 12 x 2 = 24  minutes and for the last 2 metres he takes 1 minutes. Therefore he takes 24 + 1 = 25 minutes to reach the top.

9.    (2)
Solution:
Let the distance PQ = A km.
And they meet x hrs after the first man starts.
Average speed of first man = A/10 – 6 = A /4 km/hr
Average speed of second man = A / 12 – 8 = A / 4 K/hr.
distance travelled by first man = Ax/4 km
They meet x hrs and the first man starts. The second man, as he starts 2 hrs late, meets after ( x- 2 ) has from has start. Therefore, the distance travelled by the second man = A(x-2) / 4 km
Now , Ax/4 +  A (x-2) /4  km = A
x = 3 hrs.
They meet at 6 a.m. + 3 hrs = 9 a.m.

Shortcut: (Try this your self)
= Starting time + [ ( Time taken by first ) (2^nd’s arrival time – 1^st starting time ) ] / (sum of time taken by both)

10.  (1)
Solution:
Let the total distance be x km.
Time taken at the sped of 80 km/hr = x/80 hrs.
Time taken at the sped of 60 km/hr = x/60 hrs.
He rested for ( x/60 – x/80) hrs = 20x / 60 x 80 = x/240 hrs.
his rest per hour = x/240 ÷ x/60 = ¼ hrs. = 15 minutes.