Question

Match the fractions given in Column I with the shaded portion of figures in Column II

Column I	Column II
\[\left( i \right)\dfrac{6}{8}\]	(p)
\[\left( ii \right)\dfrac{6}{10}\]	(q)
\[\left( iii \right)\dfrac{6}{6}\]	(r)
\[\left( iv \right)\dfrac{6}{8}\]	(s)

(a) (i) – (p), (ii) – (q), (iii) – (s), (iv) – (r)
(b) (i) – (s), (ii) – (p), (iii) – (r), (iv) – (q)
(c) (i) – (r), (ii) – (s), (iii) – (p), (iv) – (q)
(d) (i) – (p), (ii) – (q), (iii) – (s), (iv) – (r)

Answer 1

Hint: To solve this question, we will consider all the options in column II and then calculate all the values of elements p, q, r and s in column II and then match it with the column I. Also, we will make the fraction of the given element of column II and then solve it. The fraction can be calculated by using the formula, \[\text{Fraction}=\dfrac{\text{Shaded Blocks}}{\text{Total Number of Blocks}}.\]

Complete step by step answer:

Consider part (p) of column II. It is,

The fraction of (p) can be calculated using
\[\text{Fraction}=\dfrac{\text{Shaded Blocks}}{\text{Total Number of Blocks}}\]
\[\text{Fraction of p}=\dfrac{6}{8}\]
Hence, (p) matches with option (i).
Now, similarly consider part (q) of column II.
It is,
(q)

The fraction of (q) can be calculated using
\[\text{Fraction}=\dfrac{\text{Shaded Blocks}}{\text{Total Number of Blocks}}\]
\[\text{Fraction of q}=\dfrac{6}{10}\]
Hence, (q) matches with option (ii).
Now, again similarly, consider part (r) of the column (II). It is as,
(r)

The fraction of (r) can be calculated using
\[\text{Fraction}=\dfrac{\text{Shaded Blocks}}{\text{Total Number of Blocks}}\]
\[\text{Fraction of r}=\dfrac{6}{8}\]
Hence, (r) matches with option (iv).
Now, again similarly consider option (s) in column II. It is as,
(s)

Fraction (s) can be calculated by using
\[\text{Fraction}=\dfrac{\text{Shaded Blocks}}{\text{Total Number of Blocks}}\]
\[\text{Fraction of s}=\dfrac{6}{6}\]
So, (s) matches with option (iii).
So, we finally have correct answer as,
(a) (i) – (p), (ii) – (q), (iii) – (s), (iv) – (r)
Hence, option (a) is the right answer.

Note:
The possibility of a mistake in this question can be at the point where (r) of column II is considered.
(r)

Students can add all the blocks together which is 4 + 4 = 8 and total number of shaded blocks = 4 + 2 = 6. So, the fraction becomes \[\dfrac{6}{8}.\]