NCERT Exemplar Solutions - Class 6 - Mathematics - Unit 8: Ratio & ProportionFill in the Blanks
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Question. 35
35. A ratio is a form of comparison by _____.
Answer
A ratio is a form of comparison by division.
Step by Step Solution
Ratios compare two quantities by dividing one by the other.
Question. 36
36. 20 m : 70 m = Rs 8 : Rs ____.
Answer
20 m : 70 m = Rs 8 : Rs 28.
Step by Step Solution
Simplify \(20:70=2:7\). Let \(8:x=2:7\Rightarrow x=\dfrac{8\times7}{2}=28\).
Question. 37
37. There is a number in the box \(\square\) such that \(\square,\;24,\;9,\;12\) are in proportion. The number in the box is ____.
Answer
There is a number in the box such that 18, 24, 9, 12 are in proportion. The number in the box is 18.
Step by Step Solution
Proportion means \(\dfrac{x}{24}=\dfrac{9}{12}=\dfrac{3}{4}\Rightarrow x=24\times\dfrac{3}{4}=18\).
Question. 38
38. If two ratios are equal, then they are in ____.
Answer
If two ratios are equal, then they are in proportion.
Step by Step Solution
Equality of two ratios defines a proportion: \(a:b=c:d\).
Question. 39
39. The ratio of the perimeter of the boundary of the shaded portion to the perimeter of the whole figure is ____.
Answer
The ratio is 3 : 7.
Step by Step Solution
From the grid (each square of unit length), the outer boundary has perimeter proportional to 28 units, and the shaded boundary has 12 units. Thus \(12:28=3:7\).
Question. 40
40. The ratio of the area of the shaded portion to that of the whole figure is ____.
Answer
The ratio is 1 : 6.
Step by Step Solution
Whole figure has 24 unit squares; shaded region has 4 unit squares. Hence area ratio \(4:24=1:6\).
Question. 41
41. Sleeping time of a python in a 24 hour clock is represented by the shaded portion in Fig. 8.3. The ratio of sleeping time to awaking time is ____.
Answer
The ratio is 3 : 1.
Step by Step Solution
Shaded portion shows 18 hours sleeping and 6 hours awake. \(18:6=3:1\).
Question. 42
42. A ratio expressed in lowest form has no common factor other than _____ in its terms.
Answer
A ratio expressed in lowest form has no common factor other than one in its terms.
Step by Step Solution
In lowest terms, numerator and denominator are co-prime (gcd = 1).
Question. 43
43. To find the ratio of two quantities, they must be expressed in ____ units.
Answer
To find the ratio of two quantities, they must be expressed in same units.
Step by Step Solution
Units must match before comparing by division.
Question. 44
44. Ratio of 5 paise to 25 paise is the same as the ratio of 20 paise to ____.
Answer
Ratio of 5 paise to 25 paise is the same as the ratio of 20 paise to 100 paise (i.e., 1 Rupee).
Step by Step Solution
\(5:25=1:5\). For \(20:x=1:5\Rightarrow x=100\) paise \(=1\) Rupee.
Question. 45
45. Saturn and Jupiter take 9 hours 56 minutes and 10 hours 40 minutes, respectively for one spin on their axes. The ratio of the time taken by Saturn and Jupiter in lowest form is ____.
Answer
The ratio is 149 : 160.
Step by Step Solution
Convert to minutes: Saturn \(=9\times60+56=596\) min; Jupiter \(=10\times60+40=640\) min. Ratio \(596:640\). Divide by 4: \(149:160\).
Question. 46
46. 10 g of caustic soda dissolved in 100 mL of water makes a solution of caustic soda. Amount of caustic soda needed for 1 litre of water to make the same type of solution is ____.
Answer
100 g.
Step by Step Solution
Maintain the same ratio (grams : mL): \(10:100= x:1000\Rightarrow x=10\times\dfrac{1000}{100}=100\) g.