NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 8: Ratio & Proportion - True or False Questions
Question 22

Question. 22

5 kg : 7.5 kg = Rs 7.50 : Rs 5

Answer:

false

Detailed Answer with Explanation:

  1. We are checking if the two ratios are the same:
    (;5 ext{ kg} : 7.5 ext{ kg};) and (;₹,7.50 : ₹,5;)
  2. A quick way: change each ratio into a fraction and simplify.
    For the first ratio:
    (;dfrac{5}{7.5};)
    Remove the decimal by multiplying top and bottom by (10):
    (;dfrac{5 imes 10}{7.5 imes 10} = dfrac{50}{75};)
    Now divide by (25):
    (;dfrac{50div 25}{75div 25} = dfrac{2}{3};)
    So, (;5 ext{ kg} : 7.5 ext{ kg} = 2 : 3;)
  3. For the second ratio:
    (;dfrac{7.50}{5};)
    Remove the decimal by multiplying top and bottom by (100):
    (;dfrac{7.50 imes 100}{5 imes 100} = dfrac{750}{500};)
    Now divide by (250):
    (;dfrac{750div 250}{500div 250} = dfrac{3}{2};)
    So, (;₹,7.50 : ₹,5 = 3 : 2;)
  4. Compare the simplest forms:
    (;2:3;) and (;3:2;)
    They are not the same.
  5. (Optional cross-check using cross-multiplication)
    Compare (;5 imes 5 = 25;) with (;7.5 imes 7.5 = 56.25;)
    Since (25 eq 56.25), the ratios are not equal.
  6. Conclusion: The statement (;5 ext{ kg} : 7.5 ext{ kg} = ₹,7.50 : ₹,5;) is false.
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