Counting of figures– Railway Reasoning (part – 1)

Total Questions: 50

31. How many triangles are there in the given figure? [RRB JE 23/05/2019 (Evening)]

Correct Answer: (b) 28
Solution:

Here triangles are, abd = 3, efg = 3,
behc = 8, cdfh = 8
And (abh), (adh), (ceg), (cfg), (ecf), (bdh)
Hence it has 3 + 3 + 8 + 8 + 6 ⇒ 28
triangles

32. How many rectangles are there in the given figure? [RRB JE 24/05/2019 (Morning)]

Correct Answer: (c) 30
Solution: Formula for finding the number of rectangles :- ( C₁ + C₂ + …… Cₙ ) × ( R₁ + R₂ + …… Rₙ )
In the above figure a rectangle can be possible only in the highlighted portion so for finding the rectangle firstly find number of rows and number of columns and then add each row and column in reverse order and after that multiply the sum of column and rows.
So in this figure number of rows = 2, number of columns = 4, sum of rows = 3, and sum of column = 10
Hence from formula = 10 × 3 = 30
So this figure has 30 rectangles.

33. How many squares are there in the given figure? [RRB JE 24/05/2019 (Afternoon)]

Correct Answer: (a) 15
Solution: In the above figure abcd has 5 squares similarly efgh and ijkl also have 5 squares
So, Total number of squares in above figure is 5 + 5 + 5 = 15

34. How many triangles are there in the given figure? [RRB JE 24/05/2019 (Evening)]

Correct Answer: (c) 22
Solution:

Here afbe has 4 × 2 = 8 triangles
adcf has 4 × 2 = 8 triangles
and other triangles are = (aeg), (ahd), (bif), (fjc), (abc) and (def)
Hence total triangle in the above figure
= 8 + 8 + 6 = 22

35. How many triangles are there in the given figure? [RRB JE 25/05/2019 (Afternoon)]

Correct Answer: (c) 12
Solution:

Here triangles are :- (afd), (fdc), (fce), (fbe), (abf), (abd), (abe) , (acf) , (aec) , (fbc) , (bdc) (abc).
Hence total triangles in the above figure = 12

36. How many squares are there in the given figure? [RRB JE 25/05/2019 (Evening)]

Correct Answer: (a) 17
Solution:This type of figure has 5 squares so there are 4 such figures in the given question
But the highlighted part is common in all the figures so this common part will be subtracted from the total number of squares.
Thus, total number of squares in the given figure = 5 × 4 - 3 = 17

37. How many squares are there in the given figure? [RRB JE 29/05/2019 (Morning)]

Correct Answer: (b) 18
Solution: Trick for finding squares :- firstly find number of rows and columns and then apply
(Cₙ × Rₙ ) + ( Cₙ - 1 × Rₙ - 1 ) + ……….. (Cₙ - ₙ × R n - n )
In this figure rows = 3, and column = 3
So (3 × 3) + (2 × 2) + (1 × 1) .
⇒ 9 + 4 + 1 = 14
So the total number of squares in this figure = 14 + 4 (outer square) = 18.

38. How many triangles are there in the given figure? [RRB JE 29/05/2019 (Afternoon)]

Correct Answer: (c) 27
Solution: Here Triangles are :- EKM, LFN, EOR, OFR, EFR, IKO, ILO, IKL, PRJ, JRQ, PQJ, IMR, INR, IGJ, IHJ, IDR, ICR, IDC, AIG, BIH, DGP, DMR, HQC, NRC, AIJ, IBJ, ABJ
Hence total triangles = 27

39. How many lines are there in the given figure? [RRB JE 01/06/2019 (Evening) ]

Correct Answer: (c) 17
Solution:

Here lines are
Vertical = 5 , Horizontal = 4
Slant = 8
Hence total lines are = 5 + 4 + 8 = 17

40. What is the minimum number of lines required to make the given figure? [ALP Tier II 21/01/2019 (Morning)]

Correct Answer: (a) 9
Solution:

Minimum Number of lines required to make the given figure = 9