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

false

We are checking if the two ratios are the same:
(;5 ext{ kg} : 7.5 ext{ kg};) and (;₹,7.50 : ₹,5;)
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;)
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;)
Compare the simplest forms:
(;2:3;) and (;3:2;)
They are not the same.
(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.
Conclusion: The statement (;5 ext{ kg} : 7.5 ext{ kg} = ₹,7.50 : ₹,5;) is false.