RBSE Class 6 Maths Important Questions Chapter 12 Ratio and Proportion

Rajasthan Board RBSE Class 6 Maths Important Questions Chapter 12 Ratio and Proportion Important Questions and Answers.

RBSE Class 6 Maths Chapter 12 Important Questions Ratio and Proportion

Multiple Choice Questions

Question 1.
If the cost of 10 pens is ₹ 40, then cost of 12 pens is:
(a) ₹ 48
(b) ₹ 42
(c) ₹ 36
(d) ₹ 40
Answer:
(a) ₹ 48

Question 2.
If the sides of a triangle are in the ratio 1:3:5 and its perimeter is 90 cm, then the length of its smallest side is :
(a) 20 cm
(b) 30 cm
(c) 10 cm
(d) 5 cm
Answer:
(c) 10 cm

Question 3.
The ratio of boys and girls in a school is 7 : 9. If there are 63 girls in the school, then the number of boys are :
(a) 63
(b) 40
(c) 45
(d) 49
Answer:
(d) 49

Question 4.
Choose the correct statement:
(a) 5 : 8 > 3 : 4
(b) 5 : 8 < 3 : 4
(c) 5 : 8 = 3 : 4
(d) None of these
Answer:
(b) 5 : 8 < 3 : 4

Question 5.
In a camp, 550 men had food provisions for 20 days. For how many days will it last long for 220 persons?
(a) 50
(b) 45
(c) 60
(d) 55
Answer:
(a) 50

Question 6.
If a, b, c and d are in proportion, then :
(a) ab = cd
(b) ad = bc
(c) ac = bd
(d) None of these
Answer:
(b) ad = bc

Question 7.
4.5 : 20 :: x : 10, then the value of x is :
(a) 2.25
(b) 2.75
(c) 2.85
(d) 2.5
Answer:
(a) 2.25

Question 8.
The lowest form of 150 : 45 is :
(a) 10: 3
(b) 15 : 3
(c) 3 :10
(d) 12 : 5
Answer:
(a) 10: 3

Fill in the Blanks

Question 1.
A ratio is compared by ......................
Answer:
division

Question 2.
Two ratios are equal, then they are called in ......................
Answer:
proportion

Question 3.
A ratio has no ......................
Answer:
unit

Question 4.
If 2 : 3 : : 12 : ........, then the value comes in box is ......................
Answer:
18

Question 5.
If four numbers are in proportion then ...................... of extremes is equal to ...................... of means.
Answer:
product, product

State whether True or False

Question 1.
12 : 18 : : 5 : 6
Answer:
False

Question 2.
A ratio is a unit less quantity.
Answer:
True

Question 3.
The two terms of a ratio cannot be of different units.
Answer:
True

Question 4.
If ad > bx, then \(\frac{a}{b}<\frac{c}{d}\).
Answer:
False

Very Short Answer Type Questions

Question 1.
Ravi types 480 words in 8 minutes, how much time he will take to type 540 words?
Answer:
Time taken to type 480 words = 8 minutes
∴ Time taken to type 1 word
= \(\frac{8}{480}\) = \(\frac{1}{60}\) minutes
∴ Time taken to type 540 words
= \(\frac{1}{60}\) × 540 = 9 minutes.

Question 2.
A car travel 234 km in 6 hours. How long will it take to travel 663 km?
Answer:
Time taken to travel 234 km = 6 horns
∴ Time taken to travel 1 km
= \(\frac{6}{234}\) = \(\frac{1}{39}\) hours
∴ Time taken to travel 663
= \(\frac{1}{39}\) × 663 = 17 hours
Hence, for travelling 663 km, car takes 17 hours.

Question 3.
The first, second and fourth terms of a proportion are 36, 81 and 63 respectively. Find the third term.
Answer:
Let the third term be x.
Then, 36 : 81:: x : 63
Product of extremes = Product of means
36 × 63 = 81 × x
⇒ x = \(\frac{36 \times 63}{81}\)
⇒ x = 28
Hence, the third term of the given proportion is 28.

Question 4.
Find the value of x, if 55:11:: x : 6.
Answer:
55 : 11 : : x : 6
∵ Product of extremes = Product of means
55 × 6 = 11 × x
x = 30
⇒ x = \(\frac{55 \times 6}{11}\)
⇒ x = 30

Short Answer Type Questions

Question 1.
If 22.5 metres of uniform iron rod weights 85.5 kg, what will he the weight of 5 metres of the same rod?
Answer:
∵ Weight of 22.5 metres of iron rod = 85.5 kg
∴ Weight of 1 metre of iron rod = \(\frac{85.5}{22.5}\) = \(\frac{855}{225}\) kg
∴ Weight of 5 metres of iron rod = \(\frac{855}{225}\) × 5 = 19
Hence, weight of 5 metres of iron rod = 19 kg.

Question 2.
A bag contain rice which is sufficient for 60 persons for 3 days. For how many days would the rice last for 18 persons?
Answer:
For 60 person food is sufficient for = 3 days
For 1 persons food is sufficient for = 3 × 60 = 180 days
For 18 persons food is sufficient for
= \(\frac{180}{18}\) days = 10 days
Note: Less men will take more days to finish the food, while more men take less days to finish the food.

Question 3.
Find the following ratios in the simplest form:
(i) 3 min : 120 seconds
Answer:
We have 1 min = 60 seconds 3 min : 120 seconds
= (3 × 60) sec: 120 sec
180 : 120 = \(\frac{180}{120}=\frac{18}{12}=\frac{18 \div 6}{12 \div 6}\)
{∵ HCF of 18 and 12 = 6}
= \(\frac{3}{2}\) = 3 : 2

(ii) 1 m : 90 cm
Answer:
∵ 1 m = 100 cm
1 m : 90 cm = 100 cm : 90 cm
= \(\frac{100}{9}\) = \(\frac{10}{9}\) = 10 : 9

(iii) 1 week: 3 days
Answer:
∵ 1 week = 7 days
1 week: 3 days = 7 days : 3 days
= \(\frac{7}{3}\) = 7:3

(iv) 900 g: 2.5 kg.
Answer:
∵ 1 kg = 1000 g
2.5 kg = 2.5 × 1000 g = 2500 g
900 g : 2.5 kg = 900 g : 2500 g
= \(\frac{900}{2500}\) = \(\frac{9}{25}\) = 9 : 25