NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 8: Ratio & Proportion - Multiple Choice Questions
Question 1

Question.  1

The ratio of 8 books to 20 books is

(A)

2 : 5

(B)

5 : 2

(C)

4 : 5

(D)

5 : 4

Detailed Answer with Explanation:

  1. Write the ratio as a fraction:
    ( dfrac{8}{20} )
  2. Find the greatest common divisor (GCD) of 8 and 20.
    Factors of 8: (1,,2,,4,,8)
    Factors of 20: (1,,2,,4,,5,,10,,20)
    Common factors: (1,,2,,4)
    Greatest common factor: (4)
  3. Divide the numerator and denominator by (4):
    ( dfrac{8 div 4}{20 div 4} )
  4. Simplify each part:
    ( dfrac{2}{5} )
  5. Write the fraction back as a ratio:
    ( 2 : 5 )

So, the ratio of 8 books to 20 books in simplest form is (2 : 5).

Quick check of other options (optional)

(5:2) means ( dfrac{5}{2} ), which is larger than (1); but ( dfrac{8}{20} = 0.4 ) is less than (1).
(4:5) means ( dfrac{4}{5} = 0.8 ), not (0.4).
(5:4) means ( dfrac{5}{4} = 1.25 ), not (0.4).
Therefore, only (2:5) matches.

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