Question 1 1 / -0
A man facing west turns 45° clockwise, then 180° clockwise and then 270° anti-clockwise. Which direction is he facing now?
Solution
Clearly, the man initially faces the direction OA. On moving 45° clockwise, he faces the direction OB. On further moving 180° clockwise, he faces the direction OC. Finally, on moving 270° anti-clockwise, he faces the direction OD, which is southwest. Hence, the answer is (4).
Question 2 1 / -0
I am facing east. I turn 100° clockwise and then 145° anticlockwise. Which direction am I facing now?
Solution
As shown in the figure, you initially face east, i.e. the direction OA. On turning 100° clockwise, you face the direction OB. On further turning 145° anticlockwise, you face the direction OC. Clearly, OC makes an angle of (145° - 100°), i.e. 45° with OA.
Question 3 1 / -0
A river flows from West to East. On the way, it turns left and goes in a semi-circle round a hillock and then, turns left at a right angle. In which direction is the river finally flowing?
Solution
As shown in the figure, the river flows eastwards from A towards B, turns left and follows a semi-circular path to reach C, where it turns left and flows eastwards towards D.
Question 4 1 / -0
You go north, turn right, then right again and then go to the left. In which direction are you facing now?
Solution
The movements indicated are as shown in the figure (A to B, B to C, C to D, D to E). Thus, the final movement is in the direction indicated by DE, which is east.
Question 5 1 / -0
Samir started from his police station on inspection duty. After travelling straight for a distance of 4 kilometres, he turned left for the market and travelled straight for 600 metres. He now turned left again and travelled straight for another 200 metres, and turned left and travelled straight for 600 metres. How far is Samir from the police station?
Solution
Consider the diagram given below.
Calculate the distance between the initial and final position of Samir as shown below. Distance between the initial and final position = 4000 - 200 = 3800 m = 3.8 km
Hence, the distance between the initial and final position of Samir is 3.8 km.
Question 6 1 / -0
Kunal walks 10 km towards north. From there, he walks 6 km towards south. Then, he walks 3 km towards east. How far and in which direction is he with respect to the starting point?
Solution
The movements of Kunal are as shown in the figure (A to B, B to C and C to D).
AC = (AB – BC) = (10 – 6) km = 4 km
∴ Kunal's distance from the starting point A
= AD =
= 5 km
So, Kunal is 5 km northeast with respect to his starting point.
Question 7 1 / -0
Rohan walks 3 km towards north and then turns left and walks 2 km. Then, he again turns left and walks 3 km. At that point, he turns left and walks 3 km. How far is he from the starting point?
Solution
The movements of Rohan are shown in the figure below:
Clearly, AD = BC = 2 km
So, required distance = AE
= (DE - AD)
= (3 - 2) km = 1 km
Question 8 1 / -0
Manik walked 40 metres towards North. He took a left turn and walked 20 metres. He again took a left turn and walked 40 metres. How far and in which direction is he with respect to his starting point?
Solution
The movements of Manik are as shown in the figure below (A to B, B to C and C to D).
Clearly, ABCD is a rectangle.
So, AD = BC = 20 metres
Thus, D is 20 metres to the West of A.
Question 9 1 / -0
Namita walks 14 m towards West, then turns to her right and walks 14 m and then, turns to her left and walks 10 m. Again turning to her left, she walks 14 m. What is the shortest distance (in metres) between her starting point and the present position?
Solution
The movements of Namita are as shown in figure (A to B, B to C, C to D and D to E).
Clearly, Namita's distance from the initial position = AE = (AB + BE) = (AB + CD)
= (14 + 10) m = 24 m
Question 10 1 / -0
A man leaves for his office from his house. After walking 20 m towards east, he turns south and walks 10 m. Then, he walks 35 m towards west and further 5 m towards north. Then, he turns towards east and walks 15 m. What is the straight distance (in m) between his initial and final positions?
Solution
The movements of the man from A to F are as shown in the figure.
Clearly, DC = AB + EF
F is in line with A.
Also, AF = (BC – DE) = 5 m
So, the man is 5 m away from his initial position.
Question 11 1 / -0
A rat runs 20 m towards east, turns right and runs 10 m and then, turns right and runs 9 m. Now, he turns left and runs 5 m and then, turns left and runs 12 m. Finally, it turns left and runs 6 m. Which direction is the rat facing now?
Question 12 1 / -0
Amit walked 30 metres towards east, took a right turn and walked 40 metres. Then, he took a left turn and walked 30 metres. In which direction is he now with respect to the starting point?
Solution
The movement of Amit is as shown in the figure (P to Q, Q to R and R to S).
Clearly, his final position is S, which is to the southeast of the starting point P.
Question 13 1 / -0
Maya starts from point T, and walks straight to point U, which is 4 ft away. She turns left at 90° and walks to W, which is 4 ft away, turns 90° right and goes to P, which is 3 ft away, turns 90° right and goes to Q, which is 1 ft away, turns 90° left and goes to V, which is 1 ft away, and once again turns 90° right and goes to R, which is 3 ft away. What is the distance between T and R?
Solution
The movements of Maya from T to R are as shown in the figure.
Distance between T and R = TR
= TU + UR
= TU + PW + QV
= (4 + 3 + 1) ft
= 8 ft
Question 14 1 / -0
A man went to meet his uncle in another village situated 5 km away in the northeast direction with respect to his own village. From there, he went to meet his father–in–law living in a village situated 4 km to the south of his uncle's village. How far away and in which direction was he finally with respect to his village?
Solution
The man moves from his village at O to his uncle's village, i.e. A and thereon to his father–in–law's village,i.e. B.
Clearly,
OBA is right–angled at B.
So, OA
2 = OB
2 + AB
2 OB
2 = OA
2 – AB
2 OB =
km =
km = 3 km
Thus, B is 3 km to the east with respect to his initial position O.
Question 15 1 / -0
A person starts from a point A and travels 3 km eastwards to B. Then, he turns left and travels thrice the distance travelled earlier to reach C. He again turns left and travels five times the distance he covered between A & B and reaches his destination D. The shortest distance between the starting point and the destination is
Solution
The movements of the person are as shown in the figure.
Clearly, AB = 3 km
BC = 3AB = (3 × 3) km = 9 km
CD = 5 AB = (5 × 3) km = 15 km
Draw AE ⊥ CD.
Then, CE = AB = 3 km and AE = BC = 9 km
DE = (CD – CE) = (15 – 3) km = 12 km
Using Pythagoras theorem, we get:
In ΔAED, AD
2 = AE
2 + DE
2 AD =
km =
km = 15 km.
∴ Required distance = AD = 15 km
Question 16 1 / -0
A girl leaves home for a walk. She first walks 30 metres towards northwest and then 30 metres towards southwest. Next, she walks 30 metres towards southeast. Finally, she starts walking back towards her home. In which direction must she walk to reach her home?
Solution
The movement of the girl is shown in figure below (A to B, B to C, C to D, D to A).
Clearly, she must walk in the direction DA, i.e. northeast.
Question 17 1 / -0
Sanjeev walks 10 metres towards south. Turning to the left, he walks 20 metres and then moves to his right. After moving a distance of 20 metres, he turns to the right and walks 20 metres. Finally, he turns to the right and moves a distance of 10 metres. How far and in which direction is he from the starting point?
Solution
The movements of Sanjeev from A to F are as shown in figure.
Clearly, Sanjeev's distance from starting point A
= AF = (AB + BF)
= AB + (BE – EF) = AB + (CD – EF)
= [10 + (20 – 10)] m = (10 + 10) m = 20 m
Also, F lies to the south of A.
So, Sanjeev is 20 metres to the south of his starting point.
Question 18 1 / -0
Kashish goes 30 metres North, then turns right and walks 40 metres, then again turns right and walks 20 metres, then again turns right and walks 40 metres. How many metres is he from his original position?
Solution
The movements of Kashish are as shown in the figure (A to B, B to C, C to D, D to E).
∴ Kashish's distance from his original position,
A = AE = (AB – BE) = (AB – CD)
= (30 – 20) m = 10 m
Question 19 1 / -0
A man walks 1 km towards east and then turns to south and walks 5 km. Again, he turns to east and walks 2 km. After this, he turns to north and walks 9 km. How far is he now from his starting point?
Solution
The movements of the man are as shown in the figure below (A to B, B to C, C to D, D to E).
Clearly, DF = BC = 5 km
EF = (DE - DF) = (9 - 5) km = 4 km
BF = CD = 2 km
AF = AB + BF = AB + CD = (1 + 2) km = 3 km
∴ Man's distance from starting point A = AE =
= 5 km
Question 20 1 / -0
Going 50 m to the south of her house, Radhika turns left and goes another 20 m. Then, turning to the north, she goes 30 m and then starts walking to her house. In which direction is she walking now?
Solution
The movements of Radhika are as shown in figure.
(A to B, B to C, C to D and D to A)
Clearly, she is finally moving in the direction DA, i.e. north-west.
Question 21 1 / -0
X and Y start moving straight towards each other from two places 200 m apart. After walking 60 m, Y turns left and goes 20 m, then he turns right and goes 40 m. He then turns right again and comes back to the road on which he started walking. If X and Y walk with the same speed, then what is the distance between them now?
Solution
Clearly, Y moves 60 m from Q up to A, then 20 m up to B, 40 m up to C and then up to D.
So, AD = BC = 40 m.
QD = (60 + 40) m = 100 m
Since X and Y travel with the same speed; X will travel the same distance along the horizontal as Y travels in the same time, i.e. (60 + 20 + 40 + 20) m = 140 m.
So, X travels 140 m up to A.
Distance between X and Y = AD = (100 – 60) m = 40 m
Question 22 1 / -0
Of the five villages P, Q, R, S and T situated close to each other, P is to the west of Q, R is to the south of P, T is to the north of Q and S is to the east of T. Then, R is in which direction with respect to S?
Solution
Clearly, the location of villages according to the given directions is as shown.
So, R lies to the south-west of S.
Question 23 1 / -0
P, Q, R, S, T, U, V and W are sitting around a round table for group discussion, in the same order and at equal distances. Their positions are clockwise. If V sits in the north, then what will be the position of S?
Solution
Clearly, the seating arrangement is as shown in the figure below.
So, S is at the south-west position.
Question 24 1 / -0
The post office is to the east of the school while my house is to the south of the school. The market is to the north of the post office. If the distance of the market from the post office is equal to the distance of my house from the school, in which direction is the market with respect to my school?
Solution
The positions of various places are as shown in the diagram.
Clearly, the market is to the north-east of the school.
Question 25 1 / -0
A, B, C, D, E, F, G, H and I are nine houses. C is 2 km east of B. A is 1 km north of B and H is 2 km south of A. G is 1 km west of H while D is 3 km east of G and F is 2 km north of G. I is situated just in the middle of B and C while E is just in the middle of H and D.
Solution
Since E lies in middle of H and D,
so HE = ED.
But HD = 2 km. So, HE = ED = 1 km.
∴ Required distance = GE = GH + HE
= (1 + 1) km = 2 km.
Question 26 1 / -0
Directions:
Solution
I lies in the middle of B and C.
So, BI = IC.
But BC = 2 km.
So, BI = IC = 1 km.
So, I lies directly above E.
∴
Required distance = EI = HB = 1
Question 27 1 / -0
Directions:
Solution
From the above diagram AF = 1 km.
Question 28 1 / -0
Directions For Questions
Directions:
...view full instructions
Who is to the north-east of the person who is to the immediate left of Kunal?
Solution
Clearly, the arrangement of boys is as shown.
Clearly, Atul is to the left of Kunal and Prashant is to the north-east of Atul.
Question 29 1 / -0
Directions For Questions
Directions:
...view full instructions
If a boy walks from Nitin, meets Atul followed by Kunal, Dinesh and then Prashant, how many metres has he walked, if he has traveled the straight distance all through?
Solution
Clearly, the arrangement of boys is as shown.
Required distance = (25 + 40 + 60 + 90) m = 215 m.
Question 30 1 / -0
Directions For Questions
Directions:
...view full instructions
A is in the middle of
Solution
The villages are located as shown in the adjoining figure.
Clearly, A is in the middle of G and C.
Question 31 1 / -0
Directions For Questions
Directions:
...view full instructions
Which two villages are the farthest from one another?
Solution
The villages are located as shown in the figure below.
Clearly, F and B are the farthest from one another.
Question 32 1 / -0
Directions For Questions
Directions:
...view full instructions
How far is E from F (in km)?
Solution
The villages are located as shown in the figure below.
Required distance = FE = FA + AE = FA + GD
= (2 + 2) km = 4 km
Question 33 1 / -0
I start from my home and go 2 km straight. Then, I turn towards my right and go 1 km. I turn again towards my right and go 1 km again. If I am north–west from my house, then in which direction was I going in the beginning?
Solution
Clearly, the route is as shown in figure A
It is given that the person is finally to the north – west of his house.
Rotating figure A 90° anti–clockwise, we obtain figure B satisfying the specified conditions.
It is evident from the figure that the direction of walking in the beginning was west.
Question 34 1 / -0
After walking 6 km, I turned right and covered a distance of 2 km, then turned left and covered a distance of 10 km. In the end, I was moving towards the north. Facing which direction did I start my journey?
Solution
Clearly, the route is as shown in the adjoining diagram. Thus, the man started his journey facing north.
Question 35 1 / -0
A direction pole was situated on the crossing. Due to an accident the pole turned in such a manner that the pointer which was showing east, started showing south. One traveler went to the wrong direction thinking it to be west. In what direction was he actually traveling?
Solution
The actual positions of the directions are as shown in I while the changed positions of the pointer can be described by II.
Clearly, the direction of West shown by the pointer in wrong position (figure) is actually South.
Question 36 1 / -0
A watch reads 4.30. If the minute hand points east, then in what direction will the hour hand point?
Solution
Clearly, to show 4.30, the position of the minute and hour hands of the clock will be as shown.
So, again as shown, if the minute hand points East, then the hour hand will point in the North-east.
Question 37 1 / -0
It is 3 o`clock in a watch. If the minute hand points towards the north-east, then the hour hand will point towards the
Solution
Clearly, the hour hand points towards South-east.
Question 38 1 / -0
A clock is so placed that at 12 noon its minute hand points towards north–east. In which direction does its hour hand point at 1:30 p.m?
Solution
Clearly, the positions of the minute and hour hands at 12 noon and 1.30 p.m. are as shown in the diagram. So, as shown, the hour hand at 1.30 p.m. points towards the East.
Question 39 1 / -0
A man is performing yoga with his head down and legs up. His face is towards the West. His left hand will be towards
Solution
The posture of the man is as shown below.
Clearly, the left hand points towards North.
Question 40 1 / -0
One morning after sunrise, Reeta and Kavita were talking to each other face to face at Tilak Square. If Kavita's shadow fell exactly to the right of Reeta, then in which direction was Kavita facing?
Solution
In morning, the Sun rises in the East, so any shadow falls towards the West. Now, Kavita's shadow falls to the right of Reeta.
Hence, Reeta is facing South and Kavita is facing North.
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